Can I add a sink/lavi to the 2" vent of a toilet drain?

If you are asking about adding a bathroom sink drain to the vent of the toilet, yes, all codes that I know now allow this as long as the trap arm is within specified distances. In my area 1 1/2 can be run up to 3 1/2 feet max in the horizontal before tying into the toilet vent.

Yea, I just found out in CA you can go out up to 60". Thanks for the quick reply.

We can go 60" (five foot) with two inch, but only 42" with 1 1/2. Im under UPC, same as southern cal. Which part of cal allows 60" for 1 1/2? We have CA plumber on board here, hope he pops in to clarify this. Codes do very from area to area, even if they are under the same code book, just different areas adopt their own codes.