You don't necessary have to build pure AD to benefit from lifsteal, as long as you primarily doing damage via a method that can proc it. Tiger and Bear stance are aa modifiers I believe, and his only damage in turtle stance is aa (unless you built an active item). The stances all have windows for him to benefit from lifsteal. The only difference is that the stance with the least amount of damage offers it along with defensive stats.
Though they have an innate heal, all three of the champions you mentioned usually build lifesteal at some point in time, Aatrox being sooner than later, and all deal a good amount of damage via auto attacks which is where they benefit from it.
I think Udyr's base AD along with whatever AD he picks up from items (Trinity gives a bit as well) is more than enough to benefit with lifesteal. I can't imagine him gaining a significantly larger amount of sustain from an on-hit heal than from lifesteal, so switching just feels like unnecessary limiting the window for Udyr to build AD damage.
That just my take though.