"She could hardly finish her work for lack of time."
Translation:Ŝi apenaŭ povis fini sian laboron pro manko de tempo.
Right. More info on de/da here:
I would argue that any context that makes the first she and second her different people would make the sentence poorly written.
- "Mary was doing Sara's work, and she could hardly finish her work for lack of time."
I don't know who "she' is in my example above, but (as a native speaker) I still sense that "she" and "her" is one person.
As for "si" being "required" or not - Esperanto requires one or the other. Once you know which idea you want to express, you need to use the appropriate pronoun, whichever it is. Picking one excludes the meaning of the other.