Lynx came out the same time as the Game Boy, and Nintendo didn't have a monopoly of the market, just the right game at the right time.
Historically, that's what it takes. Super Mario Bros. (NES), Tetris (Game Boy 1st life), Sonic the Hedgehog (Genesis), Pokemon (Game Boy 2nd life), Final Fantasy VII (PSX), Halo (Xbox).
Truthfully, I don't see that coming out for any system. Just more of the same, with a bit of variation on the DS. I think that will be what really will make people take notice of either system.