What gauge plastic sheeting is used on replacing lanai windows?

replacing the window, or covering the window?

I'm bot sure why you would use plastic sheeting to replace windows.

https://www.youtube.com/watch?v=AuNjGz3LLPY

Are you talking about plastic that comes in a roll which can be stapled up as a replacement for screening? Or are you replacing glass panes with plastic ones?

If it's the sheeting I'd guess at least 6mm or even a bit thicker. Feel it and determine if it feels strong enough. It should be thick enough to not have much if any stretch to it. If you're looking for plastic window panes go to Home Depot or wherever and they have plastic panels of varying thicknesses. Pick the one that works for you. I'll say probably about 3/16"? If you know the dimensions of the windows they will cut it for you. If not, it's very easy to cut yourself.

Are you wanting something like a thin plastic sheet that is used for a shower curtain or a thick sheets of polycarbonate or acrylic that you can cut to the size of the window and install permanently?

The thickness depends on the frame it is going into and the size of your pocket. Whether you want it for external or internal use, UV protected or no! Go to the store and ask an expert there!

Find a store in your area that sells Auto Upholstery... and look for the clear plastic that is used for the windows in convertible tops... it is thicker and has a UV coating to keep it from turning dark from the sun and cracking from the cold. The cost will be higher.. but it will last a lot longer