Rulings

Lavabrink Floodgates’s reflexive triggered ability triggers and deals damage only if you sacrifice it while resolving its triggered ability. It won’t trigger if you sacrifice it for any other reason.
The player whose upkeep it is may put a doom counter on Lavabrink Floodgates, remove one from it, or do nothing.
Lavabrink Floodgates is sacrificed for having three or more doom counters on it only while its ability is resolving. If you put a third counter on it some other way, it won’t be immediately sacrificed.