This is what I gleaned from Memory Alpha (and my own memory)...
https://memory-alpha.fandom.com/wiki/Dilithium
So it was definitely a known thing by the 2360's, at the latest.
And "The Burn" sounded like a one time event, so the Discovery should be fine.
I remember the Starlog special for TNG the month before it aired mentioned that recrystalizing dilithium was really one of the big deals for the series, as they weren't going to deal with materials shortages. One of the main reasons TNG is so "utopian" (It isn't but people use the term lightly and I am no better), is directly tied to that. Of all the magic devices in Trek, this might be one of the most magical. So if there wasn't anything left for it to crystallize, that would be problematic.
I'm going to bet that the recrystallizing chamber is one of the first upgrades Discovery gets.