The first and most important ingredient I would suggest is water. A lot of products that claim to be "lip safe" claim to be non-toxic or even vegan, but actually don't contain any of the ingredients that are in your typical lip safe lipstick. The non-toxic and vegan ingredients are: hydrogenated polyisobutene, oxybenzone, caprylic/capric triglyceride, caprylic/capric triglyceride/butylene glycol, octyldodecyl stearoyl stearate, octyldodecyl stearoyl stearate/dioctyl stearoyl stearate, microcrystalline cellulose, disodium edta, isopropyl myristate, triethanolamine, isopropyl myristate/pentaerythrityl tetraethylhexanoate, methylparaben, propylparaben, sodium stearoyl glucoside, titanium dioxide, and/or zinc oxide. There are many ingredients that can be found in your usual lip safe lipstick that have no use for your eyelashes, but the most common ones are: petrolatum, beeswax, glycerin, and/or silicone. Some ingredients are more common than others, and some are found in many different types of lip safe lipstick.
Some examples of non-toxic lip safe lipstick are: Revlon Colorstay Liquid Lipstick - The "Dirty D" is a lip safe liquid lipstick that is not formulated to be worn with eyelashes. If you need a non-toxic lipstick that you can wear with your eyelashes, this one is the best one. It has an anti-aging formula that contains glycerin, cocoa butter, niacinamide, and aloe vera. This one is not safe for your eyelashes.