I always recommend saving melee LB3 until the boss is at low health, of 10%.
Else, I'd save up for healer LB3. Trust me, I've been into numerous situations of early LB3s, so I learned this the hard way.

Moreover, the one who executes LB3 are literally a sitting duck for a whole 8-10 (healers for 5 seconds) seconds when executing Melee LB3. So, you have to find the right moment for it, or risk dying to an AoE or targeted mechanics. You can try communicate who will use the LB3 and when, it'll make things much easier to manage since they will leave the LB3 to you.

As for candidates, SAMs for one are very capable of Melee LB3 due to their long duration buffs. I don't play other melee, so I can't say which other classes are good at it.