Can I file a mechanics lien as a design professional as Civil Engineer

We received a retainer based on our contract. We completed the project, billed the client, but the client refused to pay the bill, offered less. During a two month time where they would not answer my emails or texts, except a very briefly and inadequately, I learned that they did not ever sign my original contract. The original contract states that payment of the retainer is acceptance of the contract in entirety. At this point, we're at stalemate. They are not talking. No permit has been applied for that I know of. They owe a few thousand for the design work.