BennVenn recently announced his LCD mod kit for Lynx model 1 and now Mr Lurch has done a very nice installation and hardware hacking video with this kit. It's a rather more complicated install compared to the Lynx model 2, but is worth it for the image quality. We'll have a written up guide posted here soon, meanwhile here's the video...
You can order you Lynx 1 LCD mod kit from here.
Be sure to subscribe to Mr Lurch's Things channel on YouTube. If you want to see his other Lynx LCD kit videos, here are a couple of links: BennVenn Atari Lynx LCD Replacement: A new alternative and Quick Update: BennVenn's LCD for the Atari Lynx II.