Will they go after my house, if I close my account? I can't pay my other bills because they are holding my deposit?

Actually you probably can't "close" the account since it is frozen and the attachment ( garnishment) will take any future funds paid into the account. But you can ask the bank.

And while they can go after a lien, normally they want to try and get your money first, bank accounts and garnishment of your wages next.

Since the lien only allows them to get the money when you sell the property, often a lien can take years and years to get their money