Contractor threatening a lien on a property that's pending sale

[J R.]

I'm currently under contract to purchase a house that's scheduled to close in several weeks. The seller just told my agent that we should terminate the deal because one of the contractors who worked on the house has threatened to place a lien on the house. I'm wondering:

1. Can a contractor place a lien on a property that's transferred ownership if the work was contracted by the previous owner and completed prior to the transfer of ownership?

2. Would such a lien be covered by title insurance if it's placed a.) while the contract is pending or b.) after the closing?