It's only a theory... and one of the questions has to be why Capella and not Gamma Draconis?
The Knossos was in Gamma Draconis, and removing the star would
really mess up gravity in the system. The Knossos could also be destroyed, or the spinning pieces could be shifted out of alignment and hit each other. And if actually survived, it would slingshot off in one direction and get farther and farther away from the Capella node, making it necessary to perform more and more power on intrasystem jumps...if that's possible with the star destroyed (I've always figured the gravitational field of stars allows for the intrasystem jumps somehow).
That brings up an odd idea for Capella...maybe the Shivans were destroying Capella to remove the GTVA's ability for interspace jumps, rather than destroying the nodes (which they might see as holy, inviolate, or irreplaceable)?
Edit: More on topic.

The Lucy, IMHO, was the command ship of a long-term scout fleet. Basically, the Shivans seed the area with small scouting groups and when they detect vessels with a certain amount of technological level, they locate their command center and destroy it. Since it's a "first-contact" group, the primary concern would be protecting the mothership from primitive weapons, so it could continue on its mission for, theoretically, forever. (rather than be worn down by attrition)
The Shivan tactics in FS1 make sense if you go with a centralized-mind mentality, with a central "brain-bug" controlling multiple drones. In FS1 it says the Shivans were only interested in controlling jump nodes; they were, strategically, performing surgical strikes against the "brain-planets" of the Terrans and Vasudans. They probably discovered in the computers of a destroyed ship that the source of their orders was either Vasuda Prime or Terra, and made that their prime target. They then bombarded the planets in an attempt to kill whatever commanded the fleets, perhaps not realizing it could be moved.
The Lucifer is perfect for that kind of operation; shields protect it from primitive vessels' weapons as it heads towards a central planet, then it proceeds to orbitally bombard the planet's surface. Of course, the Terrans surprised them by discovering a way to track ships and subspace.
So, to sum it up, I think the Lucy was just a scouting group's command ship, tasked with destroying species before they could threaten the Shivans.