Yes, I think you are damaging your lips further each time you apply the lemon juice. Lemon, lime, orange, and grapefruit juices contain citric acid , which is a pretty corrosive acid. It exfoliates and eats into things like teeth and skin.
Because they break down the bonds between skin cells, these juices are used on their own as natural face astringents (applied with a cotton ball), and they can be part of the recipes of commercial facial astringents/lotions as well.
Citrus juices, oils and acids can actually cause lips to develop cheilitis, and they cause teeth to lose their mineral coating, which it is never possible to replace.
Don't get me wrong, these juices are very nutritious when taken internally, but they are harmful to the teeth and skin, especially with frequent contact or when left on.
I've had several dentists tell me to limit my exposure to citrus juice because they are so corrosive to tooth enamel. You should never brush your teeth within an hour after exposure to citrus juice, apple juice, pear juice, soft drinks, or vinegar-containing foods; you should wait at least an hour to give your teeth a chance to remineralize before brushing. If anyone doubts this, I have compiled at least 10 sources from dental experts explaining it, including the Canadian Dental Association, and would be happy to post them for you.
Basically, I think that you are disrupting your lip skin and stopping the healing process each time you soften and remove it with the lemon juice.
Mixing the lemon juice with honey or glycerin would make it taste sweeter and might offer your sloughed-off, raw skin a bit of comfort after the fact, but it's like taking 3 steps back and 1 step forward.
Glycerin on its own is a good healer, and perfect for cheilitis sufferers.
The main thing is to put your efforts into finding out why your lip skin is overgrowing and exfoliating in the first place, so you won't need to manually exfoliate the skin that is building up, or to glue that skin down with moisturizing products.
Bottom line though, no one should take medical advice from strangers who have no medical training and are only guessing about these things themselves based on their self-treatment; so if you have access to health care, see a doctor or at least a dentist (I have found that frequently they also have training in cheilitis and treat cheilitis of their patients) and ask him or her these questions.