The assumption that helping chickens must involve petrochemicals is incorrect. Natural organic ointments are going to do the job a whole lot better. There are countless ways to make your own lipbalm, I prefer those with beeswax myself. https://www.google.com.au/search?q=lipbalm+beeswax
Olive oil and beeswax are both things that can be eaten, I often eat a little wax when I eat honeycomb. I guess if I didn't want the organic sort of feel to it, I could gargle some gasoline as well, WAIT, be serious, no gasoline, just beeswax and olive oil. Plenty of other recipes out there from people who make lip balm at home and sell it at markets for good money.
Oh my, I'm having trouble trying not to ask the riddle, "How do you make chickens go WOOF WOOF ?" because we are after all on the topic of coating chickens with petroleum products, and that's half the punchline to that joke.
I can't see the point of keeping chickens for eggs in the first place if you're going to contaminate the eggs with poison chemicals, supermarket eggs are cheaper and laced with anything you like. Many people keep chickens just so that they can have fresh, clean food. Organic lip balm preserves that.