No mammal (indeed no land animal) lays eggs in water. The platypus, which swims and feeds in water, is a monotreme that lays eggs, but it does so in special burrows where they can be incubated. When the eggs hatch, the mother nurses the young as all mammals do.
Reptiles are all vertebrates with scaly skin, and many of them lay eggs. 70% of snakes lay eggs, while most lizards also lay eggs. Alligators and crocodiles lay eggs, and all known turtles and tortoises lay eggs.