Want to clarify that? There is no "Mac Pro G5" there's the Mac Pro and the older Power Mac G5, and the latter wouldn't be able to run 10.7. The Mac Pros all use Intel CPUs, not a variant of the PowerPC family like the G5.

So assuming you're attaching an old Cinema Display to a new Mac Pro via some kind of an adapter, then my first thought would be simply that some change to the graphics subsystem has caused a problem with your old monitor. It may fix itself in a subsequent update, but most likely it's only going to get worse with time. Do you have a spare monitor, Apple or otherwise, that you could connect to your Mac Pro to see if the problem persists?