It causes a little confusion to have that "Blank Space" right after the the main verb "expect" because we cannot be sure that it represents that a blank or a space is that follows, or that Blank Space is used as a noun.
To answer this question I will assume that blank space represents that a line goes there to be filled.
By doing so, the correct sentence would be:
Joel and Lucy expect _their_ Halloween party to be really scary!
So the final answer is:
Their
The possessive third person plural pronoun is the best option.