This is possibly a very complex problem with various answers. Here's a few ideas for you to think about:
Generally, as long as this lab is medically ok, it's highly likely the dog needs behaviour replacement.
If the previous owner didn't teach the dog about correct behaviour and it sounds to me like so, that needs to be corrected.
Clearly your other dog knows and is possibly trying to correct that behaviour but failing. Or it is more likely that there is a power struggle between the 2 big dogs. This possibly means your Australian dog has been in charge all along and the top dog position is being challenged.
Dogs are pack animals and need to be lead as well as being told what to do. You need to lead and bring the pack together. If you lead all 3 dogs by being the top dog, they will follow and respect each other if you do.
I have rescued difficult dogs my whole life and I regularly get calls from the local rescue centre to help families with these problems. In my experience, unless there's a medical problem, it's almost always behaviour or lack of training.
A lab is a working dog and needs exactly that. Their brain must be challenged as well as their physicality... like all dogs!
Here's a few links for you to look at but I can guarantee that this dog needs training and behaviour control. If you put the effort in, this dog and the others, as well as you will have a relationship you didn't think would exist:
The best book I ever read: