is there a way to get LB3 by my own?

[Canadane]

Just incredibly disappointed they put all this work into job specific limit breaks that'll never get used because you're not melee dps.

Just hit the button before a melee does. The only thing to be disappointing in is your trigger finger speed.
Unless it's content that requires specific utilization of the limit break, it doesn't really matter who ends up using it. You more than likely won't cause a problem in the fight.