Why would they even want that ship, or assume they can take control?
There were other options that could have made sense as an explanation. In a deleted scene in the pilot, Rush reveals there are legends regarding the treasures that await on the other side when one dials the ninth chevron, speculating that it was for this reason the Lucian Alliance attacked Icarus. They could have had the Lucian Alliance still after these treasures.
Another, comes from the episode Life where we learn that the Icarus planet originally belonged to the Lucian Alliance. Revenge is a bit simplistic a motivation, but a logical one.
Instead they went and depicted the Lucian Alliance as the galaxy's self-appointed defenders dead-set against the planet Earth. And to make matters more stupid, they know all about Destiny and what it is, thanks to Telford. But they still want it anyway since it's an Ancient starship. You want an Ancient starship? Find a way to enhance a ha'tak so it can reach the Pegasus galaxy and obtain one of the dozens that are just drifitng around there. They're probably in better working condition than Destiny.