Most of the time on bosses, melee DPS will use their LB as it does a fair amount more damage than the equivalent mage LB. Unless there are adds to burn down it should always be the melee DPS LBing where a damage LB is required. Weapon damage also seems to play a role so have the best geared DPS fire the LB. By the way, in most boss encounters you'll want to ensure the LB is fired off as soon as the bars fill. In a longer fight this will allow the opportunity for a second weaker LB near the end. From my experience as well you shouldn't bother burning a 1 bar LB at the start of a fight in most cases. For the melee LBs at least, 2 LB1s is equal more or less to an LB2. May as well build the LB2 and get the bigger bang later in the fight. Plus frontloading damage in some boss fights will cause them to skip phases/mechanics that will throw off your routine (Garuda skipping a jump is a good example).