Using lysol to mop floors around puppies is it bad..

You wouldn't be mopping floors when puppies were present. You would be doing it, and rinsing well, when they are somewhere else. Yes, not a good idea to expose them to chemicals.

Tick

Vinegar and water are a good cleaner as is any mild soap and water. Harsh chemicals simply not necessary.

Vinegar and water is a great solution, but I have always used Lysol on my floors. In fact Lysol has an ingredient called bitter X which tastes very, very bitter to both animals and kids. It's a safety precaution to avoid accidental ingestion.

When my dogs were pups, they used to chew on electrical wires or my running shoes. I wiped the cords down with the solution and voilà! No more shoe and cord chewing.

Of course you are going to be diluting the Lysol in water when you wash the floors, so unless you are letting your dog walk on the wet floors, or he is allergic to the product, you shouldn't have any issues at all.