Congratulations, guys!
Though I haven't owned a Lynx since the first year of release, it was and remains one of my favourite pieces of tech - both for the hardware and the software.
Whilst some could correctly argue that other formats hosted more accurate conversions (be they arcade ports or previously computer-based titles), the Lynx had my favourite versions of several games. I'm not sure how they'd hold up to a newcomer all these years on, but the titles listed so far (particularly the early ones) are the ones that I'd recommend and hope to return to come the day that I can once more own the console. It'll just be a shame that multi-player gaming among friends will no longer be possible... Three of us had a Lynx at that time, so it's a much-loved period in my gaming life.
Given your list, famicommander, it's difficult to add recommendations without an unknown-for-me "Get most of them!"; but I can second shadow460's findings and suggest that you look for RoadBlasters. I had reasonable access to the arcade game back then and tried both the Megadrive/Genesis and Amiga versions, yet the Lynx one is the one that I was always happy with and played regularly from the game's purchase until the time that I moved on to other, non-portable hardware. A friend at the time thought a lot of APB, too. Though there's a bit that I like about it, it's not a game that I've ever been a great fan of (in any incarnation) - but I believe that the Lynx does a reasonable job of replicating the original.
Moving away from games that you may have already played, Electrocop is something different.
Of course, for further arcade thrills there's also Pit Fighter. Nah, just kidding - I'm not that cruel!
Okay, I'll play nice and add two more!
Shadow of the Beast and Robotron 2084. The former is a fair conversion of the Amiga original, though perhaps one to stay away from if you're more about gaming than witnessing something for technical reasons. Robotron? Er, it's Robotron - it has to be loved!
Given that I could add a few more and do need to go, I'll end it there before I end up leaving you a book to read! Enjoy your consoles and the games, guys. I'm interested in hearing more from you, once you've had some time with them - particularly if the Lynx is new to you.
Happy gaming!