I'm assuming that you want or need some sort of lip stuff either for moisturizing purposes or for cosmetic purposes.
If simply for moisturizing purposes, then certainly a clear substance such as chapstick, chopsaver, etc. should do the trick.
If for cosmetic purposes, that's tricky because almost anything will smear from the mouthpiece pressure and movement. I'm not sure that anything will withstand that stress, but I also don't think the the guys (who typically don't use lipstick) on this forum will provide much insight.
I do wonder whether one of the high-end (and more expensive) lipsticks or glosses (like Ulta's Stila Stay All Day) might do the trick. But I'm skeptical of this.
It's a real bind -- because the substances that will stay on and not smear are substances that don't actually moisturize and provide flexibility.
I think the real question is whether you REALLY need the colored stuff on your lips while you're playing. It seems unrealistic to expect to play a performance (of, say, over an hour) and have ANY visible lip coating still intact.
In terms of a true solution, I suppose you could consider tattooing your lips the appropriate color -- but that of course (aside from the cost and discomfort of the procedure) would require a permanent commitment to a specific color -- which is a pretty heavy commitment and trade-off.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)