Short Answer:  Yes, you can usually file a mechanics lien for as little as $1.  No, there are not usually any minimum amounts required to file a lien.  However, be cautious as specific state rules may vary.

Long Answer:  Filing a mechanics lien carries some expense, and so as it with every type of legal remedy, one examining the mechanics lien remedy must consider whether the "juice is worth the squeeze."  Is the cost of the mechanics lien, in other words, worth it in light of the result you will receive.