Anyone have experience with this? What varnish/lacquer would you recommend? Any tips?

I haven't had any hands on experience with this, but others have posted about doing that kind of thing with their X-Wing pieces and/or to use superglue around the exposed edge to toughen it.

Here's the thread:

https://community.fantasyflightgames.com/topic/190547-protecting-my-shiny-new-game/

You might try spray on varnish, usually found in the paint department at the hardware store. I don't remember where I read it, but I believe floor varnish (acrylic) was also suggested. Don't ruin your tiles because of my bad advice though!

Test whatever you end up going with on some chip board, cardboard, or even better an old board game that you wouldn't care too much if something happened to it like your kid's Memory Game tiles since they have similar construction.

Good luck and post your results!