Rare prisms and crystallized lore

You usually get crystallized lore from events (usually towards the end of the event as a final reward or event shop reward)

Definitely don't burn servants for lores. You usually get 1-3 per event. Last year I got maybe 25, but didn't get all possible because my account was too weak on my first few events.

Burning gold summoned servants is the only way to get rare prisms. Welfares don't give rare prisms, though eventually we'll get an update that if you get 6+ copies of a welfare in a rerun then you will get a rare prism in your present box. Not sure when NA will get that update.

Crystallized lores are primarily event rewards; the ones in the RP shop are basically just for whales.

You'll get 36 crystallized lores in 2019, assuming you complete everything in all events.