Effect of paying off a lien

This is not the way to go. While you could sue later, the chances of winning that lawsuit are slim after paying off the lien, and the chances of collecting on any eventual judgment are even slimmer. 

The better method is to "bond off" the lien. You may be able to take out a loan with the same mortgage company for this specific purpose. Otherwise you can obtain a Mechanic's lien bond from most sureties. The premium on a bond is typically 10% or so, which makes this a more economical option.