you might have to be a licensed mechanic to get a mechanic's lien but you can lien a vehicle when ever it's left on your property. I do this for when I buy a vehicle that has gone through a bunch of hands and doesn't have any paper work left. I just say it's been sitting at my house for a couple years.
If the dude dropped it at your place and knew where you were and didn't come to get it it's his fault.