If they are not licensed not only would they lose but also you can disgorge them from evey penny you paid them. See a construction lawyer to consult.
Business and Professions Code 7031(a) and (b) are very powerful if they apply. Under section 7031(a), an unlicensed contractor cannot sue to recover any money under law or equity for services and/or materials provided. Thus, such an unlicensed contractor should not be able to enforce a mechanic's lien and could be liable for abuse of process for filing an invalid lien. In addition, under section 7031(b), an unlicensed contractor must return all money paid, even if they did a good job. Finally, you may also wish to file a complaint with the California State Contractor's Licensing Board. They may help you resolve your dispute with the contractor.
You indicate that this individual "is suing" you. If they have filed a lawsuit you may be able to dispose of it through a legal motion known as a "demurrer" depending on how the complaint is drafted. There are certain legal requirements and deadlines involved in a demurrer and various other legal procedures that arise in litigation.
If you have actually been sued and served you really should not try to handle this yourself and should retain a real estate lawyer to assist you.
IMPORTANT NOTE: This response was prepared by Adina T. Stern, A Professional Law Corporation for informational purposes only and is not intended as legal advice. The information available in this answer is not intended to create, and receipt of it does not constitute, an attorney-client relationship. The information on legal issues available here is not a substitute for legal advice from an attorney who is familiar with all of the facts surrounding your particular situation who is licensed in the appropriate jurisdiction. This answer does not create an attorney-client relationship.
You may have claims for abuse of process or malicious prosecution for filing a lawsuit that does not have merit. Those claims are not easy to establish or prosecute so you should contact an attorney.
If the contractor was not licensed at the time the work was performed, then you would be entitled to disgorgement of all amounts paid, and the contractor would not be able to enforce his claims against you.
The lack of a written contract can be a problem, but is not really that big of a deal for you. It is a bigger problem for the contractor.
You really need to contact a construction attorney in your area for a consultation.
I have an office in Santa Monica and one in Montclair. I do not charge for short consultations and would be happy to talk with you about your matter. 909-455-1194.