Translation:Though she loves him, she does not want him.
Well, first of all, you have "non lo vuole". "Lo" (him) is the object of "volere" so it is clear that someone does not want him, not her.
Now we need to verify who the subject of the second part of the sentence is.
While it is true that Italian doesn't generally makes use of pronouns (as subject and in front of a verb), they are expressed when the meaning becomes unclear. So if the subject was to be changed from "lei" to "lui", then "lui" would have been used "lui non lo vuole" (making the sentence a little bit odd because of the "lo").
I wrote: "despite she loves him, she doesn't want him" I was marked wrong and was given this answer: "Despite that she loves him, she doesn't want him." Mr. DL to whom write the English sentences pleas be advised that after despite you don't use that. Please see this: We don’t use a that-clause after in spite of or despite. https://dictionary.cambridge.org/grammar/british-grammar/in-spite-of-and-despite
I agree that you cannot use a "that" clause after despite. You need to say either "despite loving him......" (i.e. using the present continuous of a verb after "despite") or use a noun object as in "despite her love for him.....". This is also what your quoted reference offers as the two ways of using "despite".
Saying "despite she loves him..." is not correct English as you are using a clause (ie. she loves him) as the object of a preposition. However I put "despite loving him....." (which is correct) but it was still not accepted by Duo as they wanted us to use "though".
If you use the subordinating conjunction "though" as Duo wants us to then you can follow it with a clause, as in "though she loves him....." but that is not the case with "despite", which is a preposition.
As a final note, the alternative but wrong solution provided by Duo could be made correct by inserting "the fact that" instead of just "that' (i.e Despite the fact that she loves him.....) because you then have a noun ("the fact") as the object of "despite". However I think "despite her love for him...." is a better example of a noun object.