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.
The correct answer is "they're". If the question was in first persons point of view, it would have been "our" but sense the question is third point of view, the correct answer would be "they're". Its not "their" because its not just one person, its both Joel and Lucy, meaning there is more then one person, so I would say it is "they're" :)
