Yeah I don't think ANYTHING works well on the Lynx, Nomad, Game Gear, and Turbo Express. They are ALL battery hogs from hell.
It's amazing how far handheld battery life has gotten. My DS Lite amazes me sometimes, seems like it goes FOREVER! Hell, any Nintendo handheld has always had good battery life. Even the original Gameboy Classic (Good life for back then anyways, but still not too bad).