Does keras' model.fit() remember learning rate when called multiple times? Let's say I'm using the Adam optimizer, and calling fit() on my model multiple times. What parameters does the fit function remember? 

From what I've observed, the loss function/metrics seem to resume from the same value (because the same saved weights are iterated on), but does the value of the learning rate reset? Does it resume from the same value it ended on the last fit() call?
Provided that you are in the same scope, will remember not only the learning rate but the current state of all tensor, hyper parameters, gradients and so on.
In fact you can call fit many times instead of setting epochs and will work mostly the same.