The Last Don 2 continues the story of the Last Don 1. Essencially, Don 1 will explain why the characters on the first book came to be that way.
There are some references to events which occured in the first book, but it's still a great film without knowing the plot. I must say, for the most part the plot of Don 1 is barely used in Don 2. For completeness, I say read the book of Don 1
{or the film of Don 1 ...if one was made} to have a better understanding. You will learn how Bethany became autistic, the murder of Athena, Pippi Crosses father & Dante, Rose Maria hating her family, Cross and the Don {who appears as a ghost} in the Don 2 only if you read the Don 1