Typically, one of the melee (monk,dragoon) or caster (black mage, summoner) will use the LB at the end on the boss or to meet a dps check.

Healers and ranged dps have a healing lb, but it is only used at endgame content to ressurect the entire party and prevent a wipe. These are most commonly used in trial content where the LB bar is immediately reset when they initiate the fight anyway, so the healing LB is just considered "better than nothing".

Tanks almost never use their LB, with the exception of one specific move (of great strategic value) in the Ultima HM fight.