In general, Melee LB has the highest priority. You also don't want to save it until the boss is already at 1-2% (Because a lot of that damage will be wasted in overkill) - use it as soon as it's full, and safe to, on a given boss. If there are no melee, Caster LB should be used. If the only DPS are bards, what the heck, do whatever.

When you advance onto later content, you'll be able to LB3 instead of LB2, and a big distinction is that healer's LB3 will immediately raise everyone, which other levels of LB won't. When this happens, you generally save melee DPS until the last 4-5%, at which point it's clear you'll clear - but until then LB3 is often saved for emergency saves.

Tank LB3 and Caster LB3 are also ideal for certain boss fights for various reasons, and a handful of advanced fights will use these LBs over the standard priority for very specific situations.