Pronouns

Pull out the proper nouns (Lisa and Mark), and you can see what's wrong:

Some of the work for I has to be reassigned to him.

Your second pronoun ("him") is fine, but as you can see above by how awkward that sentence sounds, "I" (a subject pronoun) should be changed to "me" (an object pronoun), since it's the object of the prepositional phrase "for (Lisa and) me." So the full sentence would read:

Some of the work for Lisa and me has to be reassigned to Mark and him.

Hope that helps!

I shall have hade not is entertained