Starfleet ships are rather delicate, unless your talking about the defiant or the enterprise e. The serenity would die. Voyager would get wiped out rather quickly (although i love it's phaser placements). Babylon 5 would be interesting idk anything about it though. And the death star would probably be on equal grounds with the lucifer, but would utterly destroy the lucifer. The deathstar has no problem penetrating shields. Also fs2 beams appear to have a lot more raw power to them than star trek phasers. In star trek nobody has a phaser bank that's an uber phaser of doom ever that would compare to the output of a lucy beam or a death star laser.
Also i really don't think voyager would get wiped out fast because voyager has defensively weak shields with one power source unlike the very offensive and strong shields of the 5 power source lucy. Something says it'd eventually be a standoff between the deathstar and the lucy, although i really don't know how babylon 5 would factor in at all.