The Lucy had what were referred to in FS1 as "flux cannons," which were forerunners of the modern FS2 beam weapons. Once we observed these cannons in action during the First Great War, I doubt it was long before Terran and Vasudan scientists managed to come up with their own prototypes and installed them on GTVA cap ships sometime before 2367.
I doubt the Lucy's flux cannons were reverse-engineered as such. Remember, the Lucy was the only Shivan ship with flux/beam cannons during FS1. The Lucy exploded in the Sol system and cut off Earth from the GTVA. With the Lucy debris stuck at Sol and beyond the GTVA's reach, the GTVA would not have anything to reverse-engineer. To reverse-enginner something, you have to have it in front of you so you can take it apart and see how it works. If the Lucy debris is in Sol, which has been cut off from the GTVA, then, by definition, the GTVA can't examine it.
And the scientists at Earth can't talk to the rest of the GTVA to tell them what they learned from the Lucy debris because the people in Sol can't use their subspace radios to contact the rest of T-V space, because the subspace node was collapsed. Take a look at the tech database; everything about Earth in there says specifically that all contact (including "subspace radio", if that's what it could be called) with Earth was lost. No ships could get through, no transmissions could get through, not even spitwads could get through (although that last really doesn't mean much as I've never encountered anyone who could propel spitwads across several light years. Go figure.)