that orion scooter there is probably a lot like the first one pictured, and most likely has solid tires, too. i have a few of those tires around here, collected with the motors and stuff, maybe going to go on the front of my fourwheel trailer.
good news is it's an invacare scooter, probably, so it likely has tough motors in it if they are not worn out already. most of these are setup to run 24v using 2 bit u1-size sla agm or gel batteries, around 6 or 8mph, for like 20 miles or more. also they're usually meant to carry at least 400 pounds of person and cargo on them, in additon to the scooter's own weight.
so again if you replace the sla with lithium at a higher voltage, maybe 48v, and a cotnroller to match, it'd probably do pretty well, assuming it's a 4pole motor which it almost certainly is since they hve lots more torque than the usual 2pole wheelchari motors.
keep in mind the motor will get hotter at the higher voltage if you draw the same current thru it, so if you go lots faster on it than it originally did then the motors will probably need active cooling fans of some type.
most of the these motors are environment-sealed, so cooling the insides where it's important is going to need a filter on the air coming in or it'll get dirt and dust in there you don't want especially with brushed motors.
on crazybike2 the motor hangs down at the bottom of the frame so that air passing under and around the bike frame cools it off, but that air is right off the road surface so in summer it gets kinda hot.

i wanted to eventually do some active cooling of it but have yet to get that far.