So, for a plausible idea.
Heated pet blanket
https://www.amazon.com/Homello-Waterproof-Electric-Adjustable-Resistant/dp/B07JGP75ZX/ref=
Draws 50 watts on HIGH. 28 watts on LOW
600wh battery pack $300
https://www.amazon.com/Portable-Station-Generator-Outlets-Emergency/dp/B09HHFFL7L/?_
So, running on high, full time gets you 12 hours. Put the mat in the lizard's cage.