Welll.... The atari Lynx is a portable game system. It has a display, battery, buttons and integrated "computer" for the game-play.
The raspberry pi is also a computer. But it is designed to be connected to a modern HDMI monitor, not the small LCD on the Lynx. It is designed to be connected to a keyboard not the buttons on the Lynx. It is designed to work from a 5V powersupply, not the battery in the Lynx.
So... Playing games on the pi should be possible, but not by putting it inside an atari Lynx case and hoping it will start working.
Think of trying to put a Ferrari motor inside a Fiat 500. You cannot just open the hood and click it in. There is no way it will fit. All the connections are all different.
In theory, a very talented mechanic might be able to pull it off. Change almost everything inside the Fiat to accommodate the bigger motor. But I suspect that you're not that talented mechanic.
