I tried so many different ship setups but I'm simply unable to finish this one (on Medium).
The ship setup that came the closest to winning for me was assigning Hercules fighers with Prometheus cannons and Hornet missiles to everybody. I took an Ursa bomber for myself with Prometheus cannons and 6 Harbinger missiles. I had one wing protect Delta 1, 2 and 3, leaving 4 unprotected. In the previous mission, I lost 2 Hercules fighters, (my wingmen killed each other with friendly fire - nearly unavoidable with 6 Prometheus cannons each).
I used the afterburners to zoom ahead and destroy enemy fighters, using my wingmen only as a last resort (who were on guard duty), to preserve them.
Once everybody got near to the Lucifer, I used the afterburners to zoom to the front of the ship and took out destroyed it's Weapons sub-system. I don't know if that made a difference, as I noticed that at least some turrets were still firing. I thought of taking out the 2 fighter bays but they appeared to be invulnerable (no damage % indicator).
Delta wing destroyed Reactors 1 - 4 while I pounded on Reactor 5 (which was in the front of the ship) with harbingers. All my wingmen died and finally I died before I could destroy reactor 5.
I noticed that each harbinger only dealt around 10% damage to reactor 5!! Is there anything special about this reactor? Or am I hitting it from a wrong angle? The 'X' that normally comes when the subsystem is blocked or on the other side of the ship did not appear. It normally takes only 1 harbinger to destroy a reactor.
This mission is (appropriately) the hardest. How did you folks succeed? What ships did you choose for yourself and your wingmen? What strategy did you take? And what difficulty setting was it on?
Thanks,
Valrog

Sorry for the duplicate post. I didn't know this mission was called "Good luck". It doesn't have a name in the briefing.

Its not a problem, just wanted to point it out to you so you can see if any of the suggestions in the thread help you complete the mission. I have not had the chance to play the game myself, way to many games to play at the moment, will get to it eventually though.

Ohh I keep hearing how great they are its just a matter of time, not enough of it and way to many games to get through. Just finished the redneck rampage series and then they release Divine Divinity here and I'm a sucker for action rpg style combat. Once I'm in the mood for a space sim I'll grab them both and play them through to completion.

FreeSpace 1 is good, FreeSpace 2 is awesome. Dunno about GameSpot, they keep redoing their rating system, and I'm pretty sure FS2 didn't score that high (still an awesome game, though).
Lucifer, Lucifer... Let's see... I believe I used a Herc fitted for escort to finish this mission. I know I spent most of my time trying to intercept the fighters and hoping I wouldn't get hit by a missile. If I recall correctly, you need to order the bombers to take out the reactors manually - don't worry if it takes a while between each, even a human pilot wouldn't be able to get to the reactors at every opportunity.
I did finish the mission by destroying the last reactor by myself, though. Think the bombers ran out of Harbingers. If you just get into the right position even your "lethal" weapons will be able to do good damage.
Bah, I'm not much help. Also, I won't end this post by wishing you Good Luck... dammit.

You're right. My memory was bad. It did score third-highest, though. I also don't agree with their ratings all the time. But they're a good indication of a game's quality.
Thanks for the tip. However, it didn't give me the option to give orders to Delta wing (the bombers). They're the only wing I can't issue orders to.
On one attempt I did take only bombers (I took a Hercules fighter myself). But they just died without hitting any targets, despite issuing an attack order on the reactor subsystem. Only Delta wing did any damage for some reason. Perhaps I'll try this strategy again and pay attention what went wrong. Thanks again.
Another strategy I'm thinking of doing is disabling the Lucifer by taking out both it's engines. I was able to do this quite easily, but while I was at it Delta wing died, so I restarted the mission. That was a mistake. I believe that I should be able to kill the Lucifer by myself if I manage to kill all those fighters it launches, once it's disabled so it can't exit subspace.