I have Chessies, but have kept Labs here, and can truthfully say that Labs don't shed near as much as Chessies do.
That having been said, there's some things you can do. You can start by brushing your dog *outside* every day. This not only keeps that hair down, but your dog can go longer between baths, and you will be hands-on with your dog every day. You can identify lumps, bumps, ticks, etc. Check the ears while you are at it. That way, you can stop an ear infection before it gets too far.
Offer to do the vacuuming yourself. Your dog, your dog's hair, your responsibility.
Lisa