Here's
my thread on my setup. Are you talking about this setup?
https://www.boatliftanddock.com/product/706/lift-mate-dc-12v-wheel-assist-motor
Very different than what I ended up with. You already have the lift? Looks like it was made for 12v, and 13a is a lot less than the 30-60a per motor that I'm using. The friction lift that I saw has a 11:1 reduction, or 22 turns of the big wheel for 1 drum turn, which is about 1' of travel. Then you'd have the reduction of the friction wheel-->large wheel, not sure what that is.
@72drptop said that you only needed it to run 1.5 minutes? That seems like you'd get very little lift in that amount of time, what are you basing that off of?
Anyway, I think it would probably work, is probably very slow. If you want to use a dewalt battery, you could just get a 12v system. (Any idea of the amp draw of their tools? I couldn't find it with a quick search). Other ideas would be a tractor battery or a bigger lead acid with a small/cheap solar setup. If you wanted to get more exotic, I bet you could find a li-ion 12v pack that's cheaper than the dewalt.