Does landlord (apartment) have to sign the lease in order for it to be legal?

California.
I signed a lease today. I got a copy. I have not moved in yet. I've just been told that my father has 3 months to live (he lives in the midwest). I looked over my lease agreement, to see if I had 72 hrs, and noticed that the landlord (office manager?) didn't sign where she was supposed to. So, can I get out of the lease, and just lose my deposit? Or will I have to pay the full 6 months? Is there a 72 hour clause?

There should be a clause that says you can renig any contract within 72 hours - buyer's remorse clause. I'm sure if you explained the situation to your potential landlord, they would understand, especially b/c you haven't moved in yet. They can easily get another renter, and they haven't lost anything b/c you only just signed the lease today, so there should be no penalty to you.
BTW - sorry to hear about your Dad. Best to you.

Generally speaking, it has to be signed. But how can you be sure she didn't just give you a blank copy?

no.

3 working days not weekends ,you have to break contract ,no one signed go back .have them give you $ back

Even if the landlord didn't sign the lease...which he probably has a signed original for himself...any judge would see your signature as a legal intent on renting the apartment for 6 months and hold you to the lease. There are NO rescission laws on rental agreements in any state...