It depends. Some of them use inserts that allow you to move from 1 8 TPI to 1 1/4 8 TPI. Others don't. There are also some adapters that allow you to step down:

https://www.amazon.com/Woodworking-Lathe-Headstock-Spindle-Adapter/dp/B09CY8P1GJ/ref=sr_1_2?crid=2FOX0TN04O0TM&keywords=1+1%2F4+to+1+inch+wood+lathe+adapter&qid=1674751437&sprefix=1+1%2F4+to+1+inch+wood+lathe+adapter%2Caps%2C659&sr=8-2