To accurately diagnose it, they sedate the dog and put a scope down the throat to visually examine the larynx. That said, your dogs symptoms do sound a lot like LP. Jolie and now Mulder most likely had/have a fairly mild case. They never coughed (or cough in Mulder's case) but both had a lot of noisy breathing and Jolie in particular was very weak in the rear. The restlessness is not necessarily typical of LP - that's more likely to be pain. There's nothing to say that he can't have both back problems and LP though as both are quite common in elderly Labs.
The problem is, outside of surgery there isn't really much you can do about it if it is LP other than manage the symptoms by keeping them cool (heat makes it worse), calm (excitement makes it worse) and by using a harness instead of a collar to avoid putting more pressure on the neck. If it gets to the point where you can't manage the symptoms but the dog is otherwise doing well, then it might be time to consider surgery, although that won't help the legs at all, just the breathing.
If you want to know for sure, then consult a specialist ....