What you described is called mechanics and materialman’s lien. M&M liens are a statutory scheme designed to protect a person who provides service or materials to assets. The statute’s purpose is to protect mechanics, tradesmen, craftsman, contractors, and material/parts purveyors. It protects commerce. M&M liens are allowed on cars, homes, equipment, and other assets (and an airplane certainly falls within that category) to be asserted by a person who provides the service, supplies, or parts. The person or party asserting the lien does so by filing an affidavit in the property records of the county where the asset is located (in this case, it would be with the aircraft registry records in Oklahoma City). The person asserting the lien must swear under oath that they provided either parts or materials or services that benefited the asset that they are placing the lien on, and they must itemize with some detail the value provided to the asset.
In the most simple of terms, an M&M lien cannot attach for landing fees- unless States amend the statutory scheme for M&M liens because a landing fee is not attached to the airplane. It is not a benefit or service given to the airplane. It is a charge “tax” on a privilege benefitting the individual pilot. That is why when you drive through a tollbooth and you do not pay your tolls they cannot put a lien on your car. If the toll authority is the State, they can refuse your registration renewal, but no lien. This is well established law.
Vector puts a prop lock on a plane - they will be sued, I would suggest a declaratory judgement claim - no contract and no lien - with a conversion claim added (quasi-theft) and depending on jurisdiction, a wrongful imprisonment argument is worth considering. The first two claims are eligible for fee, switching, meaning Vector will pay your attorney fees when you win.