There are actually aquatic lizards, well, semi-aquatic, available in the aquarium hobby. However, due to their warm blood, it's very unlikely they could live in cold water. I can DM you a link to a Paludarium with one in, if you wish. Unfortunately, many of the semi-aquatic lizard species are far too big to be kept in the average home aquarium. The most commonly kept are Draecana sp., often called Caiman Lizards. They are able to be kept in a large paludarium when young, and are very attractive, but unfortunately they grow to be about 5 feet in length. So unless you can provide an enclosure the size of a swimming pool, there isn't much available. People have, however, had success keeping smaller terrestrial, or arboreal, lizards in paludariums with fish.
If you are set on something aquatic, then an amphibian or some kind of terrapin would be more suitable.