Do humpback whales lay eggs

Blue whales - like all whales - are placental mammals. They give live birth and don't lay eggs.
A whale is a mammal meaning that it gives live birth. there are only several mammals on the planet that lay eggs and whales aren't one of them. So no.
No, a blue whale can not lay an egg because whales are mammals and they give live birth like all mammals do such as humans.