At normal pressure you need a high surface area silica like silica gel to have much chance at success at making your own alkali silicate but it definitely works. I've done it by boiling fumed silica with NaOH in little stainless steel dishes. Just don't let it dry out once you make it because it won't redissolve. The choice of vessel is important, boiling strong base is rather corrosive.
Lithium Hydroxide is the weakest alkali hydroxide and it may prove a bit more stubborn to dissolve the silica but I would think it could be made to dissolve even without pressure.
Also lithium is much much lighter. Expect to use a lot less of it by weight, but about the same by molecule.
Keep in mind that there is a
mixed alkali effect. Basically glasses with a combination of different alkali will soften at lower temperatures. So it is best to stick with just sodium or just lithium.
Unlike sodium silicate, I couldn't immediately find any lithium silicate sold as the pure chemical at a consumer scale either. It is used as a concrete sealer, however I wasn't able to find any online that clearly labeled their exact contents. Some of the products had MSDS which listed only lithium silicate if you wanted to go that route instead.