What are Lumin Crystals?

The important thing is what sits next to them. Glimmer is the currency you earn by playing, and it is what vendors and NPCs take for items, cosmetics and materials. Crystals never replace that. They run a separate shop that only opens if you have spent money, so nothing you do in the world builds up a crystal balance.

The two do touch in places. Sparkling Cubes cost 1,500 Glimmer or premium currency, so that is one purchase you can reach either by grinding or by paying. The Glimmer route runs through Outpost vendors: you buy 100 Sparkling Crystals and exchange them there. Anipod Ultras are also on the crystal side of the shop. Look at any premium item and check whether a Glimmer price exists for it before you decide.

What the cash shop actually sells

This is not settled yet. The shop is described as carrying cosmetics, battle passes, decorations and optional gameplay utility items, and it is also described as stopping at paid cosmetics with everything else unannounced. Those are two quite different games to spend money in, and which one launches is still open.

That matters more than the crystal itself. If the shop stays cosmetic, crystals buy you appearance and nothing else. If utility items ship, the Sparkling Cube pattern becomes the thing to watch, because it is the case where money and playtime buy the same object.

Not settled: Whether premium currency reaches anything beyond cosmetics is undecided before launch, and the full crystal price list has not been shown.