I would probably opt for two litter trays if I were you but you could always start with one and see how he gets on

I’ve not used litter trays with screens but so long as it secure I can’t imagine a liner posing a risk.

http://www.instagram.com/p/BXsXo28FTcG/?taken-by=wick_theboogeyman
— Wick has a screen, and no bottom liner. I don’t use a bottom liner because I have small granule litter, so scooping against smooth plastic works much better than a newspaper. Alternatively for cleaning, I use a spray bottle of vinegar and water (rabbit-safe, urine buster) on the bottom and wipe, as pictured in the link above. Wick does not chew or displace the screen, through there’s little room to do so. If your rabbit is doing it, you can potentially zip tie it to a sides of the litterbox (2 zip ties on opposing sides to avoid flipping screen). If you have a plastic litter box, you can safely poke holes in it by putting a screwdriver (non-metal handle, but metal head) over a flame and letting it get hot, then piercing the side of the litter box. Do so under supervision if necessary please, or have someone else do it, because the screw driver stays hot and remains hot for a while. Safer and more alternatively, perhaps you can use Command Hooks flipped upside to hook on the screen and keep it down. I’m thinking pasting them on the side, at the level where the screen falls.

Thor figured out how to lift her screen off the litter box, we went with the solution of gluing small pieces of wood in the back two corners of the box, at the level where the screen falls. That way she can’t lift it out from the front anymore. Works really well and wood is safe for her to chew, so I’m not stressing about it.

You won’t need a puppy pad – the horse stall pine pellets are really absorbent ( you only need half a cup of them ) and white vinegar mixed with water will clean the bottom of the tray up new again