Is there any way to map the controls to the mouse? Using LMB for attack would be useful.

...Not really, considering there's no way to move or change your facing with the mouse. The mouse is pretty much just for selecting options in menus -- and even there, it might not be worth it to switch a hand to the mouse just to click one or two things, given that you can use the keyboard or gamepad for that too, and have to use it for movement.
To answer your question: I imagine there's probably some esoteric software you could use to make the mouse control certain things during the "action" segments, but it's probably always going to be more awkward than just getting used to the gamepad or keyboard controls.