I am finishing my basement bath. As to the venting of the plumbing. From left to right, sink drain, toilet, tub. All drain to a lift pump. A vent is installed there. At the tub drain connection there is a 2" pipe coming up out of the floor. A vent I think. Do I tie the sink vent to the tub vent, leaving all to be vented from the lift pump vent.

The "Lift Pump" vent has to have dedicated vent. This vent has to run all the way to the roof.

You use the tub vent to vent tub and the sink. This vent can tie to another / existing vent on the 1st floor and about 48" above the floor. That vent also runs to the roof.