No, LiPos will not damage your motors. 12V is 12V, irrespective of the chemistry that produces it. A 3S LiPo is nominally 11.1V but around 12V when fully charged. Switching to LiPos will save weight (if you need to) but will be more expensive than lead acid, especially as you will need to buy a charger that will suit LiPos. A standard battery charger will not suit, but if you buy LiPos then the vendor can advise on a charger.
Frankly, if you don't need to save weight I would stick to a couple of 12V SLAs, which will be cheaper and easier - although if you haven't run the boat yet you probably don't really know if it's too heavy or not. Based on looking at the model, I suspect the builder knew what he was doing, so stick with his scheme for now. There are various sizes and shapes of SLA available, depending on their capacity (ampere/hours), so check the dimensions will fit your battery compartment(s). Component Shop is one vendor who does a variety of SLA sizes.
Greg