The Atari Lynx can be emulated on a number of platforms. There are emulators for macOS, Linux and Windows as well as game consoles, mobile phones and other handheld devices. Most of the emulators are based on the original Handy Lynx Emulator.
Emulation requires ROM files, which are dumps of the cartridge data, to be loaded into an emulator to play games. There is a big selection of these available for download from AtariAge. Some emulators also require the Lynx System ROM file being present.
If you don't have your own ROMs, most of the games in the game database have been preloaded and can be played by visiting that game's information page and clicking 'Play Online'.
The easiest way to get started with Lynx emulation on PC or Mac is to install RetroArch and use its configuration screens to download one of the Atari Lynx 'cores'.
Once the 'core' is loaded, the content i.e. ROMs can be selected.
Once a ROM is selected it can be launched and played.
Thanks to Lee Chapman, the admin of the Atari Lynx Fans for information on the GP2x.
Atari Lynx can be emulated on other consoles. Consoles like the SNES Classic Mini can be soft-modded to run emulators, including Lynx emulators. See this article on how that can be achieved - How to run Atari Lynx games on the SNES Classic Mini.Older consoles like the Sega Dreamcast can also emulate Atari Lynx. There is some discussion on this topic and the emulation information is a little hard to come by. However what is known is that an emulator called M.E.S.S. exists and can be downloaded. Since Dreamcast makes it so easy to run homebrew software, all that is needed is to burn a CD and the emulator should work.