Probably just excitement and it sounds as if the Lab hasn't really learned bite inhibition. Lots of dogs will get excited if another dog is picked up - I think they sort of see it as a toy, plus of course the chase/prey drive is triggered by frustration that they can't get to it.

Similarly, frustration at not being able to get to the dog on the other side of the fence may mean that the Lab "takes it out" on the Beagle (although it's still not really aggression as such).

That's what it sounds like, anyway.