Situation: client breached contact and now refuses to make final payment. They filed a complaint and claim on surety bond. We filed a Mechanic's lien. Then they asked for arbitration for the lien. It is in the contract that we use arbitration if there is a problem, but it doesn't specify if that applies after the lien has been filed.
This is relatively common. You should file the lawsuit to foreclose the lien while complying with Code of Civil Procedure 1281.5 to make sure that you don't waive your right to enforce arbitration (although that seems not to be an issue because they want to arbitrate). Arbitration is often preferable to court actions, but the specifics depend on your situation.
I would recommend contacting an experienced construction attorney to talk you through your options.