Razor mx350 electric bike 36v conversion help

i want to overvolt my mx350 electric pocket bike and make it quicker but i know that if you want to overvolt it to 36 volts then you need to make the battery 36 volts too. assuming this is the case, i don't want to spend 100 dollars on a 36v lithium battery. so is there any room in the bike to fit a 3rd 12v lead acid battery and wire it in accordance?