Sounds like some weird displaced behavior (too much excitement when you get home so they attack?) or some other dog weirdness.... so I agree with Jag that management would work to help the Lab for the time being.
Have you started up with any formal dog classes yet. Because there is actually alot going on here and it's not just the 'easy' part of 'I come home my dog attacks the Lab'. That's the easy part to fix (remove the Lab from the situation) but that's not the explanation for the BEHAVIOR.
My dogs would never do what your did. And though I'd like to think it's cause they are just so wonderful (and they are) it's also cause they know they could NEVER do that in front of me. NEVER. I do not allow my dogs to, in front of me, CHOOSE to leave me and go to attack a dog that is just sitting there.
My dogs KNOW I would not allow this behavior. If they even had those thoughts, they wouldn't act on them because they know it's not acceptable and mom is wading in and they are in trouble.
And it's not that I'm going to beat them or anything.... just that it's not permitted and I am extremely clear. I'm not clear during the fight, there's no clarity in a fight.
I'm clear when my dog takes one weird posturing step towards another that I don't like.
This means it's up to me to learn what is 'normal' and how my dogs and others behave so I know when to react and not. The time to act and TEACH is BEFORE the fight starts when the dog still has a brain in the game. That's when I teach them that the posturing and rude behaviour isn't acceptable, so we never even get to a fight stage.
Have you purchased and watched the DVD 'Calming Signals' by Turid Rugaas? Best video I know that taught me the tiny and small dog movements and behaviors to watch for to keep me ahead of the game.
Meanwhile, dog classes are a vast help to give us the leadership role in our pups life so they learn to look to and get information and guidance FROM us. Rather than what they otherwise learn which may be to ignore us and do what they want to do.... which can be trouble