Just from a straight comparison, though, the Lilith is 33% slower than the Cain. That would suggest that the Cain shunts as much as 50% more power to it's engines (not allowing for any scale/efficiency gains). Assuming that they have identical power output, all of that free power could have been directed straight into the Lilith's beam.
Personally, I think the Lilith is more likely to have an improved reactor as well, making it a bit more believeable that it can support that beam. No canon support for this, of course...
The reduced speed also gives it one key weakness - if it arrives outside of beam range, interceptors will almost always kill the beam turret before it can get to killing distance, just because it is so much slower than a lighter cruiser.