RE:RE:Back of the napkin Spot isn't what is used to calculate FCF or NPV, rather a barometer of price trend. The spot price you quoted represents a tiny volume of sales, not what majors are selling their annual output at, as another user just mentioned. 25-30k is what should be used for any kind of valuation attempt. I expect this to remain elevated and continue upwards for the remainder of the decade.
You also mention LiOH (hydroxide) which LAC isn't selling. LAC will be left with about 3500 MT of LCE after Ganfeng/Bankchak get their take of our total 19k (@ "market prices" whatever that may be is TBD). Hypothetically LAC could attempt to sell that 3500 @ spot, effectively paying off their mine in 1 year but time will tell.
As per output timeframes, many are under the assumption that 40k tonnes magically appear once CO begins to production. This is not the case and again as this user brings up, ramp up takes a lot of time, I'd be surprised if they're up to fully production capacity by YE23.
disclosure: very very long LAC, this one's a once in a gen station type 'trade'.
Cheers!