I strongly suspect a greyhound lacks enough buoyancy for swimming so your Lab X Greyhound may have the same problem.
My Puff is lean and when I finally was able to get her swimming, only her head and some of her neck were visible above water. That's a contrast with my Bess, chunky, bench line -- an inch or two of her entire back was visible above water along with the upper half of her tail.
Suggestion: I take it that your dog likes retrieving. Tie a strong thin rope onto a retrieving dummy and throw it into very shallow water for your dog to retrieve several times. (The attached line is so that, if you toss it too far in for your dog to get, you don't have to wade in after it -- just reel it back in and try again.) Do this several times so your dog gets used to the water and splashing.
The following days, throw it slightly farther so it requires wading in deeper water.
Before you ever try getting your dog to swim, get a flotation vest for him and put it on him for water retrieves. RuffWear's FloatCoats are among the very best.
When I was teaching Puff to swim (at first w/o the life vest) I almost had to go in after her because she was flailing the water with her front legs trying desperately to keep her head above water, body vertical in the water, not using her back legs.
That's when I got the RuffWear FloatCoat. That helped enormously. She learned to swim properly and can swim, if necessary, without wearing it. But when we go sailing, she always has it on.
HTH