The great thing about the Lynx, is there are so many genre's to choose from.
I personally enjoy most of the arcade ports. Its great to pick up the Lynx and have a quick blast.
STUN Runner, Rygar, Hydra, Battlezone 2000, Paperboy, Roadblasters, Rampart...the list goes on.
You can't go past all the Epyx games too. Blue Lightning, Electrocop, Gates of Zendocon, Chips Challenge, Zarlour Mercenary etc.