The third choice is the only one that works grammatically. It is somewhat confusing (for reasons I will explain below), but people do talk this way and it will be easily understood. Let's analyze it. It is a compound sentence, composed of two independent clauses joined by the conjunction "before". Since the meaning of "before we can move in" is clear, we can ignore that clause and just concentrate the first clause, "A lot needs doing to the house":
SUBJECT: "A lot"
VERB: "needs"
DIRECT OBJECT: "doing" (present participle acting as a noun)
SUBORDINATE CLAUSE: "to the house"
"A lot" here means "a lot of work" or "much work". Even if you don't say the word "work", it is implicit. "Work" doesn't need to be said because the speaker's intent is obvious. However, the sentence is easier for us to analyze if we replace "A lot" with "Much work":
"Much work needs doing to the house".
When we rephrase the sentence this way, its awkwardness becomes more glaring. It becomes clear that "to" is not the best preposition. We can construct more natural sentences using "for", "on", or "with".
You could tie the clause closer to "work" by moving the clause to the beginning of the sentence:
"For the house, much work needs doing."
Now that we understand what's going on, we can put "a lot" back in:
"For the house, a lot needs doing."
I think this is an improvement. The original sentence with "to the house" was confusing because the clause "to the house" was trying to play multiple roles. On the one hand it was trying to be the object of the present participle "doing". At the same time it was trying to modify the unspoken word "work" or the spoken word "lot".