I looked at precision levels and, as an amateur, I thought they are pricey for something I won't use much.
Then I got to thinking..... Why should a lathe be exactly level ? Everything is relative to the axis of the lathe. Basically you want the headstock to point to the tailstock and the carriage to tram to the axis.
So you need to ensure the bed is not distorted. No twist sag or bow. You also need to ensure that cutting forces don't cause distortion.
A lot of this checking could be done with a laser system that fits on the spindle pointing at a tailstock centre. If you can adjust out any wobble and get the laser to align on the axis when you turn the spindle 360deg then the first part is done. next you need to check the tool path is parallel to the axis by mounting a plate with a pinhole at tailstock centre and run the carriage up to the headstock. If the laser beam goes through the pinhole and shines on the tailstock the length of the travel, then all should be ok.
Let me know (politely) if I have got it wrong, I am not an engineer.