The hatshepshut wastes the hecate in 1 on 1 combat. The hecates are like wwii aircraft carriers in that they have decent point defense, weak big guns, and have massive combat squadrons and good command ship capabilities. I love their little dual towers in the back. The vasudan ships are more like battleships.
Anyway allow me to speculate on the Lilith some more: The shivans had what amounted to the only shield game in town until the terrans and vasudans stole the tech. I imagine that the capital ships like the lilith were just used against ships and installations with good anti-fighter defense since the shivan fighters and bombers could dispense with anything smaller than a destroyer with no losses (assuming alpha 1 is somewhere else). By freespace 2, gtva fighter and bomber wings are as good as or superior to shivan fighters, so they can take air superiority and blast any cruiser out of existance without even calling in a bomber wing. The lilith is deployed where fighters aren't and alpha 1 only sees 1 in the entire campaign.
Most shivan capital ships take the anti capital ship approach and would need a strong fighter escort. If they are fighting against unshielded fighters with ML-16's like the ancients, terrans, and vasudans before they discover shields, its a complete turkey shoot.
The hecate is a good strategic ship in response to shivan ships. You've got 7 engines so you can always theoretically jump out even after losing an engine to keep the ship out of a shootout with another big cap ship, a good fighter squadron for offense, and just enough firepower to run off a cruiser or help the escorting corvettes that actually do the majority of the cap ship fighting. Jumping the sathanas with the colossus's weight in corvettes would have made for a quick allied win.
I'm rambling.
Anyway, the lillith makes sense if treated as a specialized ship in a campaign doing something like following around a moloch as an assault escort. Even with the hull and LRed, its a cruiser which only poses enough anti fighter weaponry to be considered an annoyance to the fighters a hecate launches. The hecate just has to stay out of range of the Lillith and launch an assault wing.