Limit breaks are shared by the party. Once someone uses it, the bar will empty. What the limit break does depends on who uses it.

Usually it is best for a melee dps (lancer/pugilist/rogue) to use the LB, as theirs is a single target damage attack. Sometimes the caster dps (thamaturge/arcanist) is needed, as theirs is an AoE attack.

If things are getting dicey and things aren't looking good, the healer (conjurer) or archer can use the LB for a party heal.

Very rarely will the tank need to use the LB. Theirs puts up a shield for the party. It doesn't last very long.