Well, I haven't even thought about .219 Zipper for at least 20 years, which might indicate it is not at the top of the popularity lists right now. Ammo has not been made for many years, though it can be made from 25-35 or .30-30. It was a hot number when brought out by Winchester in the 1930's and is still in about the .223 class. It was designed as a varmint round for lever action rifles, and would still be good in that role.
I don't know of any reason that conversion could not be done, though I have never done it and don't know anyone who has. I think it safe to say the conversion won't be cheap and will add that unless one is dedicated to using a lever action rifle, there would be more practical ways of obtaining a good varmint rifle.
Jim