Here are some calculations based on actual numbers from an E10S encounter. A 95th percentile NIN averaging 23,544 DPS over the course of the fight performed a Chimatsuri for 898,482 damage.
According to Fürst Blumier of Allagan Studies, LBs are subject to a ±5% damage range. So for the sake of argument let's assume 898,482 was at the maximum end of the range and it's possible it could have done as little as 812,912.
According to the same document, 1 LB3 = 3.5 LB1 and 1 LB2 = 2.2 LB1. The total animation locks for each LB are lock1 = 5.86s, lock2 = 6.86s, lock3 = 8.20s.
Minimum melee LB1 damage for this party: 812,912 / 3.5 ≈ 232,260
Maximum melee LB1 damage for this party: 898,482 / 3.5 ≈ 256,709
Damage this NIN could do during the lock period for an LB1: 23,544 d/s * 5.86s ≈ 137,967
Melee LB1 damage vs this NIN's normal attacks: 1.68x ~ 1.86x
Minimum melee LB2 damage for this party: 812,912 / 3.5 * 2.2 ≈ 510,972
Maximum melee LB2 damage for this party: 898,482 / 3.5 * 2.2 ≈ 564,759
Damage this NIN could do during the lock period for an LB2: 23,544 d/s * 6.86s ≈ 161,511
Melee LB2 damage vs this NIN's normal attacks: 3.16x ~ 3.49x
Minimum melee LB3 damage for this party: 812,912
Maximum melee LB3 damage for this party: 898,482
Damage this NIN could do during the lock period for an LB3: 23,544 d/s * 8.20s ≈ 193,060
Melee LB3 damage vs this NIN's normal attacks: 4.21x ~ 4.65x
A melee DD might burst for more than 1.68x their average DPS; but a burst window doesn't last ten minutes. After a few seconds the burst window is going to close and their DPS is going to drop below their average DPS, and that would be a good time to LB.
The 95th percentile NIN in the referenced E10S run never reached more than 1.95x their average DPS during a burst window, so beating out an LB2 would be right out. And mind you, these numbers are for a 95th percentile NIN. An average player will have a much higher gain from using the LB.
tl; dr: Melee LB1 is worth it outside of a burst window. Melee LB2 is always worth it.