There are two "rules of thumb" for calculating dosages on children (and pets...and pets that are like children :) ...but these do NOT apply to Lobelia (more on that below)
One dose = one drop per pound of body weight.
Make a fraction with the weight of the child over the number 150. So if the child weighs 50 pounds, that's 50/150...then reduce the fraction to the lowest common denominator (in this case, 1/3) So the dosage would be 1/3 of the adult dosage.
But with Lobelia it's different (especially with OUR Lobelia, that is VERY effective). Lobelia is an emetic (it can cause nausea/vomiting in large doses). The dosage of ALL herbs is correctly NOT based on body weight, but rather how a particular body responds. I can easily take 3 droppersful of Lobelia (approximately 90 individual drops), and I don't feel the slightest bit of nausea...but I know one adult (that is ULTRA sensitive to herbs) that took one dropperful (30 drops) and threw up (that is VERY uncommon).
So, with Lobelia, we start low and "work up". First, always do a test with one drop to test for allergic reactions. Then I'd start with a 5 drop dose...and take it from there....going up 5 drops per dose (if you need to). You can mix it with anything, in any quantity...but it will be most effective mixed with very little fluid (or none).
Lobelia causes a very unique kind of 'scratchy' feeling on your tongue...that's actually kinda of fun. If I had a lil' un around, I would definitely go for the 'drops on the tongue' dose. I'd let him/her watch us take a dose and then laugh and giggle about how cool it was and how it made our tongue feel just like a cat's tongue (or like a "sandpaper tongue"), and then take a few more drops with him/her. It tastes mostly like apple cider vinegar (the tincture is 1/2 vinegar 1/2 alcohol), but when only taking 5 drops, it's not "nasty" tasting at all...just goofy-fun with the "itchy-scratchy" tongue.
Remember, Lobelia doesn't (or I don't think it will) affect the "tickle" that causes coughing. It WILL open up the bronchials and have a gentle, overall relaxing effect. So the calming effect may stop the trigger of the cough...but I've never read of it doing that.
What WILL sooth and stop 'the tickle that causes a cough' is marshmallow root (or slippery elm)...made into a tea so that it will coat the throat. It's VERY effective, and neither tastes bad at all...just add a bit of honey (another throat soother), and even the "tickliest" of coughs will go away in a few minutes.
Also, Lobelia does NOT "sneak up on you" and all of a sudden out of nowhere you start throwing up. If you take too much, you start feeling sweaty and kind of flushed; and then if you take more, your mouth starts watering (just like it does before throwing up). The feeling goes away within a few minutes. Of course, if you START with a great big dose, it might come all at once...but not if you start low/slow and work up.
Lobelia is NOT an herb to be afraid of (in any way) - it one of THE top ten emergency herbs (it'll stop an asthma attack or seizure 'in its tracks') and it's the ONLY herb in the The School of Natural Healing that Dr. Christopher devoted an entire CHAPTER to, all by itself!