Atari Gamer offers a large selection of Atari Lynx ROMs free of charge as downloads. All of the downloadable ROMs can also be played in the Online Lynx Emulator. These ROMs are provided to you as part of our historical preservation effort (you can read about it here).
However, not all ROMs are available for download and there may be several reasons why:
Where possible, ROM downloads are available from each of the game information pages, immediately under the game rating...
The game database also has a handy option that shows you whether a game can be played online, if it's ROM is not available or if the ROM can be downloaded. This shows up as an Atari Lynx icon on the far right in the game database listing...
Keep on Lynxing and be sure to explore all of the games that have been created for this wonderful console!