Uhh, proof? There is no official canon that beams are effective against the Lucifer's shields.
Let's see, shields require energy to run right? Well the Lucifer has to output enough energy to cover the entire hull, which is probably why it had 5 reactors.
Now, granted the shields on the Lucifer are far superior than that of a fighter or bomber. However, if you force more energy against that hull than the shielding energy can compensate for, you ultimately cut through and start melting hull plating. This is what the anti-capship beam is meant for.
An anti-fighter beam probably wouldn't have the power to make it past shielding, but the strength of a BGreen/BVas, let alone BFGreen/LRBGreen, is plenty to overpower the shielding on a Lucifer. The Colossus is capable of bringing down 5-6 LRBGreens on a Lucifer all at once, you can't say that much
focused energy won't get through the
spread apart energy of a Lucifer's shields, can you?
Think of it another way:
If an SD Lucifer ever went renegade/captured by hostile forces, how would the Shivans deal with it? Call in a Sathanas and overpower the lil' traitor with its 4 BFReds
