No, Limit Break damage/effect is fixed. It deals unaspected damage of fixed potency(depending on the level) and the damage dealt is determined by the combined WEAPON DAMAGE of the participants of the encounter. I am pretty sure you are familiar with the mechanic, but I am going to elaborate just to be clear.

All MELEE DPS: LB1/2/3 respectively

Executes single attack of 2.3k/5k/9k potency of the total COMBINED WEAPON damage of the party. Better your weapons, more damage it does.

Magic DPS: LB1/2/3

Executes Area of Effect of 1.4k/3k/5.4k Potency of the total COMBINED WEAPON damage of the party

Tanks, healers, BRD.MCH... they are irrelevant
----

So only way to affect LB damage is by upgrading your mainhand weapons.