Do I need a question mark here?

If it's a statement, it needs no question mark, as statements aren't questions. However, if it's a statement it needs a statement word-order,

Lucas’s main concern was who he would take to the apostrophe party.

If you're reading that sentence as though it contains a question, with its question word-order, then yes: add a question mark, but you also need punctuation to set the question as a question:

Lucas’s main concern was, "Who would he take to the apostrophe party?"

All of that may seem overkill if all you want is a simple scene-setter for a list of potential partners, say. Setting it as an explicit question draws attention to the question itself rather than the concern about it.