Should I apply lacquer over a wall papered with book pages

You should not do this. Foam insulation (EPS, XPS, etc.) needs to be covered with drywall in order to protect it (extend the amount of time before it melts) from fire. Otherwise you are risk of being exposed to toxic fumes and melting foam should you ever have a fire. Imagine molten foam dripping from your ceiling onto you - not a situation you want to find yourself in.

The correct "solution" is to drywall on top of the foam (using furring strips, or long screws into the studs), mud/tape the drywall, prime, and then apply wall paper using standard wall paper adhesives.

Definitely read up on the EPA 'renovation repair and painting' rule.

Option #3, the 1/4" drywall, is likely to produce the best and cleanest results, at the cost of loss of room space and alteration in the look of all your trim. You'll have to extend all outlets also. Of course that sounds suspiciously like what happened last time. Eventually your room will be solid wall covering with no center.

Option #4 sounds attractive if that texture on the wallpaper will really hold the joint compound. I'd run a test with and without the primer/sealer. Remember worst case here it cracks later and you redo it all with #3.