Those look like some late versions of Hayes Mags (Magnesium). It was the disc brake that worked and moved a lot of people over from V brakes. I'm not sure how easy it will be to find another lever, there were aftermarket ones made for awhile, Dangerboy was one brand.
You will inevitably be told to get new brakes. If the rotors are fine then a set of Shimano Deores would go straight on.
You will inevitably be told to get new brakes. If the rotors are fine then a set of Shimano Deores would go straight on.