I have a kitted Minarelli V1 bike from 1978 (which I didn't build), and a 110cc Lifan Honda Cub from 1967 (which I did build).
The kitted Minarelli goes thirty miles per hour up any hill (I could re-gear, but it's so fun), and the 110 Cub goes over sixty (but crawls up hills in second gear that the Minarelli would just eat).
They are very different machines, and both are fun.
Alex, the above said, I would spend your money on a new (well... used) Minarelli V1 plus some parts before buying a new Lifan motor for your bike.
Among other things, I do not think that your brakes are very good. The Lifan engine weighs A LOT more than the original Minarelli.
Also, the mounts for a Minarelli engine are almost two inches thinner than the mounts for a Lifan engine, and angled differently.
You would need brackets to account for the width difference, and to cut the frame (so as to not point your new engine straight at the ground like a pole-vaulter).
If you _really_ want to use that engine, buy a Honda cub frame - it is bigger, stronger, has bigger wheels with bigger brakes, and yet will leave you with something that still somehow seems like a fast, fun moped.
See if there's any interest in frame trades in the Buy/Sell forum - someone here might have a cub frame they're not using, and want an Italian moped thing like you've got.