Even though I'd love to believe that the Lucy's shields are invulnerable to beams, I am afraid it can't be.
Why?
The reason is simple: if this ship would've been invulnerable to conventional weaponry AND beams, then the Shivans would've built a huge Lucifer fleet instead of a Sathanas fleet.
Let's assume that (since the Colly is the size of 12 Lucys and a Colly is, for instance, equals a size of a Sathanas) - being really pessimistic - that you can build 8 Lucifers on the "price" of one Sathanas. If so, the Shivans could've had a fleet of 640 invulnerable ships instead of the 80 Sathanii. It is clear that the Shivans would've built the Lucys - but they didn't. Thus it is proven that the Lucy isn't invulnerable to beams.
Note: It IS possible that the Lucy needs some special resources the Shivans lacked at the time. But this is unlikely, considering the probable size of the Shivan empire and the way the canon campaigns go.