Just to make sure, did you get the EO with mint and tea tree? They have different varieties, but I think the mint and tea tree version would probably be best for the lips. It's got aloe vera, tea, calendula, and coconut oil besides the tea tree and mint, all of which are healing substances. But if you got a different variety of EO soap, that's okay - it should have beneficial ingredients too.
This is what I do --
When: After brushing my teeth (morning and evening) and anytime after eating (any meal or snack where the food or liquid gets on my lips), I wash my lips with the soap.
Also, sometimes it's not after a meal, but they just FEEL a bit hot and bothered, like they want the comfort of being washed off, so I do it then too.
What: First of all, I bend down towards the bathroom sink and spread some warm water on my lips, bringing up to my lips a full handful of warm water, to get them wet and to wash off anything relatively big (crumbs or toothpaste residue, etc.) that might be on the surface and come off with some water.
Then, I use a tiny bit of a clean paper towel (which is called 'kitchen roll' in the UK) to dab the water off my lips. I try to have the lips relatively dry before I put the soap on them, because I want the soap to be concentrated and not foam up too much.
Onto a dry finger, I pump a little of the soap out. Onto my dry-ish lips, I put the soap on with my finger. The soap is full strength, straight from the pump - no water mixed in.
(Their pumps are designed to distribute a big amount of soap on each normal pump, so I have taken to nudging the pump just a small bit to try to get only a dot of soap to come out, so that I don't waste it, and so that I don't end up with a big bunch of soap dripping off of my index finger. If a big bunch of soap does come out, I put it in a little plastic toiletry pot that I have, so I can use it in the future. Those pots cost like a pound at a shop like Muji (the Japanese store of teeny bits and bobs which has several outlets in London; don't know about the rest of the UK) - one can get a small plastic toiletry pot with lid probably also at Superdrug or Boots. Anyway, it's not necessary to have a little toiletry pot or other small container -- even a clean baby food jar with a lid on it would be fine, or an emptied and washed little blue vaseline tin -- but it helps to have something available if the pump dispenses a huge amount of soap onto your hand when you only wanted a dot of it, so you don't pour a big amount of expensive soap down the drain unused.)
After I put the undiluted soap onto my lips with my finger, I then rub the soap into my lips for about 20 seconds - this will feel like a pretty long time. It doesn't foam up because water hasn't been added to it, but it turns a bit whitish. Then, I leave it sitting there for another 20 seconds or something. I wait to feel the mint making my lips tingle, because then I can tell that the active ingredients are interacting with my cells. You could probably leave it sitting there a little longer if you wanted to.
(While it's sitting there, a little of the soap might make its way into your mouth, but I don't think that is harmful. Sometimes I can taste a touch of mint with my tongue. In that case, when I rinse the soap off my lips, I also rinse my mouth out a time or two with a handful of water.)
Then, I bend over the sink again and I rinse the soap off my lips with several handfuls of warm water, until they feel free of soap.
I dab them halfway dry with another small bit of clean paper towel, but I make sure to leave some water moisture on them, for the next step.
On damp-but-not-dripping lips, I place a small dot of glycerin/glycerine (it is very inexpensive and available from any pharmacy). You only need a small dot of glycerin. It will go on very slick and shiny -- but if you are a man, do not worry about the shininess, because it will dry to a matte texture very quickly, and in about 5 minutes it will look like you do not have anything on your lips at all.
The glycerin is important because it seals in moisture after you have used the drying soap. (Any soap is drying.)
It also is a highly recommended, safe and gentle treatment for dry and chapped lips (says this right on the bottle).
It also has been proven to coax cells that were turning cancerous into being normal and healthy again, which I think *must* help with cheilitis, even though the abnormal cell growth of cheilitis is not due to cancer (most of the time).
Glycerin also manages to slightly "glue" down your flappy, peely skin pieces, if your cheilitis has that symptom. It keeps the lip layers more stuck together and they look more presentable. But glycerin isn't a strong glue, just slightly sticky. It helps a bit with the appearance, but isn't a miracle coating. And if you eat or drink something, or lick your lips, the glycerin comes off pretty easily.
Glycerin tastes very sweet, which might feel unusual and make you worry that you are causing cavities in your teeth, but apparently glycerin kills tooth plaque on contact (I read that somewhere; not sure if it's true), so I don't mind having a little bit seep into my mouth when I'm applying it. Most of the time, it stays on my lips and doesn't get into my mouth.
I am very good about not licking my lips, so I can pretty well keep the glycerin on them until the next time that I eat or drink something. I am an earl-grey-oholic, so I have dialled back the number of times of day that I have a cup, so I can keep my lips clean and dry with the glycerin intact on them longer.
In the past, whenever I would use anything oily on my lips (vaseline, coconut oil, lipsticks, balms), I would have a compulsion to rub my lips together, because they were so slick. I think that mechanical action of rubbing them probably did no favors for my cheilitis last year, during the time when I was putting on vaseline constantly. But the glycerin actually discourages me from rubbing my lips against each other out of habit, because the glycerin makes them a bit dry and a tiny bit sticky, so rubbing together doesn't happen easily, yet they feel comfortable and hydrated.
You always need a bit of moisture (dampen your lips or dip your finger in water before putting it on) on your skin when you apply glycerin, because it absorbs moisture from its surroundings, and if you put it on dry skin full-strength and don't dilute it with water, it pulls moisture from your cells, which you don't want. If you put a bit of water on alongside the glycerin, its need for moisture is satisfied, and then it supplies the moisture to your cells over a period of time as it sits on your lips. It also draws moisture from the air.
If your cheilitis could be caused by some kind of exposure to an external substance (whether it's a food or a metal or a piece of jewelry or your fabric softener or shave gel or your own saliva or an ingredient in your friend's hand lotion, or shampoo or toothpaste or animal dander from a pet or whatever... the possibilities are nearly endless), I think that washing the lips several times a day will help the healing, because you are consistently getting rid of the invisible irritants that may be on them.
For that reason, even if you don't have any soap to hand, I still think it's a good idea to rinse your lips off with warm water after brushing your teeth and after every meal, even if you have to pop to the loo at work or at a restaurant.
And I think it's best to use a clean piece of paper towel (or toilet paper or tissue or cloth towel) each time that you wash your lips - don't reuse a towel, especially a cloth hand towel or bath towel that has been used before, because then you might transfer toiletry product residue, bacteria, even fungus to your lips from the used towel.
I also think it's a healthy, hygenic practice to use a clean pillowcase every night (or at least change it once every few nights) because a lot of oils, bacteria, sweat, saliva, toiletry products, and so on are transferred from our heads to our pillows and then back onto our skin again when we are sleeping. Multiply that nightly rubbing by the typical week or two between changing one's sheets, and one is left with an awfully grungy (microscopically speaking!) pillowcase, even the most pristine person.
I personally would not use any other moisturizer other than glycerin, but the moisturizer that you choose is a personal decision. You'll want to use some kind of light moisturizer after using the soap, or otherwise your lips could get dry and feel rough.
I feel that for me, the EO mint soap and the glycerin helped me maintain my lips in the best condition I could, whilst the cheilitis was raging -- it didn't cure my lips and it didn't stop the cause of my cheilitis, but it made them more comfortable and clean and *smoothed down* visually and tactile-ly (if that's a word) than any other treatment I had tried.
And then, when my elimination exercises over the space of several months in the autumn threw up the alpha hydroxy acids and the Boots cream as being likely causes of my cheilitis, and therefore I avoided them, and my lips began to heal, the EO soap and glycerin routine helped my lips heal faster than they would have otherwise, I feel.
The important thing in all of this is that we each need to listen to our bodies, and experiment with various suggestions that sound reasonable, ignore suggestions that sound daft, check with our doctors if anything is ever in doubt, and give a new idea some time to work (probably at least a week to give it a good go, unless it's making your condition rapidly get worse - then just stop it immediately).