There seems to be a conflict between the core rules and a sidebar piece in BFK.

The core rules state that if a ship is attacked by multiple vessels in a single turn, even if the first attacker's hits overwhelm the target's void shields, they will be up and running in time to also reduce the hits from the second attacker.

On page 25 of BFK in the sidebar on Lunar variants, the description of the Gothic-class cruiser talks about its powerful lances and how the lances don't always take out a ship quickly enough, so the Gothic is paired with escort ships who "bring down the target's defences, allowing the Gothic to finish them off." It sounds to me like the escorts overload the void shields, allowing the lance on the Gothic to get right to work... but that goes against the core rules.

Should the sidebar be dismissed as just fluff (if so, why include fluff that contradicts the rules so explicitly?), or are there components/rules that allow multiple ships to concentrate firepower into a single salvo on one target? I thought perhaps the Fleet Command Bridge would do that, but it just gives +10 to Commands between vessels.

Am I missing something or is the fluff just totally misleading?

Fluff is misleading. In Battlefleet Gothic, shields come down for the whole turn. The decision to have shields apply per ship attack in RT is largely arbitrary, but I suppose it does protect the players' ship from being easily destroyed by multiple opponents.

However, BFK has introduced squadron rules. As a squadron, a lunar class cruiser could take down the shields with it's guns, and then the lances on the Lunar and Gothic could rip the target appart.

Perhaps both are correct. In the sidebar description, if the other ship had destroyed the void shield component, then the lancer could finish the ship off quite easily.

Ahh its just a fluff problem.

BFG says gothics are great for taking down void shields (fluffwise). Since void shields simply add extra HP every turn it doesnt matter if you shoot lances or weapon batteries first.

RT has changed it the other way around. Which is perfectly ok. But Gothics are only good fleet engagements as part of a squadron. And only if you mod the RT combat system, since lances are generally worse than Macrobatteries better than Mars patterns.