I think when lava lamps were at the height of their popularity with consumers, it would have been easier to obtain specific replacement parts, like the base or the globe. It would have made good financial sense for manufacturers to keep those spare parts on hand in case of accidents. But since modern lava lamps are often marketed as nostalgic or retro items, there's no substantial demand for replacement parts. Like some other products, it's about as cheap to buy a new one as it would be to ship the old one back to the manufacturer for repair or to track down replacement parts.
The only alternative I could think of would be to visit several local garage and yard sales in search of a similar lava lamp you could cannibalize for parts, or consult an electrician or small appliance repairman for ideas on how to restore the existing base to working order.