They do not. This was stated before in interviews. It's a bonus option meant to help you recover or clear faster. Limit Break damage is never required except in rare instances like Ultimate Raids, or when attempting a new Savage Raid at the onset of it being opened, when everyone is at the minimum iLvl.
I think Yoshi said they approximately base raid boss HP off of:
-Total DPS of 4 DPS doing standard rotations + 2 tanks in tank stance (doing enmity combos) over 10-12 min with minimum ilvl.
Then, they subtract 15% from that to account for mechanics, less than perfect rotations, 1-2 deaths and then you arrive at the boss's HP. What wasn't accounted for in raid boss HP, was Healer DPS, tanks in DPS stance, stat potions, food, and limit break damage. Through those aforementioned extra things, players were able to topple new raids in min ilvl. Not intended by devs, but not unwelcomed either.
Remember, Yoshi said numerous times in past interviews that they never EXPECTED players to beat savage raids at minimum ilvl. They intentionally ALLOWED players to ATTEMPT to challenge savage raids at minimum ilvl, so they can learn the first few phases of mechanics, while simultaneously increaseing their ilvl over time from normal raid gear and tomestone gear until they have the proper DPS to clear. Hardcore players, being as clever as they are, took advantage of numerous creative ways to increase their survivability (VIT overmelds) and extra sources of damage (healers with accuracy gear; tanks with STR melds and stance dancing; stat pots, shield crit HP LB meter cheesing) to beat them. We think of it as a no-brainer now, but healer DPS was not something that even existed until final coil or Gordias Savage, really.
Devs knowing this, it's unknown if these things are now taken into account since healer DPS no longer relies on accuracy, and tank DPS has increased vastly. But I still suspect limit break damage is not taken into account, because that would presume that melee LB is the default only proper use of LB, wherein I would imagine when designing the fights, the LB is sort of a wildcard SOS type move