I built my first one hand self contained high power starter at least three decades ago using two 6 cell NiCad RC car battery packs. This was to get rid of the cord and for more power than the then popular gell-cell batteries that would not pull the skin off of warm milk. As pointed out by John, voltage is king, but I would also say as long as you use a battery system with low internal impedance.
The only problem I see with LiPo cells is that they do not like to be left with a full charge. And that whole possibility of burning down your house could be a problem. They also give up the ghost when cold, where you might need the most power from a starter.
So you pay your money and take your chances.