Because it is already time specific, one would assume "a lot" refers to the distance the person is able to swim in one hour. If they are not too concerned with the distance it could imply that they are able to swim non-stop for one hour.

In my opinion, it's not a great sentence. They should be more specific. If we're talking about time, obviously they can swim for one hour in an hour. It would make more sense to talk about distance: I can swim pretty far in an hour. But if it's a character speaking, there may be a reason that the author doesn't want the sentence to be 'perfect'.

a lot: much/many times. It means that you can do a lot of swimming (in terms of distance or just doing it a lot - continued exercise)

many miles