I am a general contractor that did an emergency tarp service on a home that was hit by Hurricane Delta in Church Point, La. The insurance company had made us aware that they allocated funds for our service based on the invoice we gave the homeowner. We did not have a contract just the invoice they needed to submit to the insurance company. The homeowner said they used that money for their deductible and since we didn't have a contract there's nothing legally we as a company can do to him.
Only a few states require written contracts in order for a mechanics lien to be filed, and Louisiana is not one of them. Further, it's absolutely possible to bring breach of contract or unjust enrichment claims against an owner when there isn't a written contract in hand. So, an owner claiming that the failure to execute a contract will leave you with no recourse is unfounded.
It's worth mentioning that, in some cases, work that doesn't provide a permanent improvement to the project property won't be lienable. However, I wasn't able to find much information regarding whether a mechanics lien would be available for tarping a roof - so it's possible the work could give rise to a valid and enforceable LA lien.
Finally, keep in mind that an official threat of a lien filing or other legal claims may be enough to get paid. Levelset discusses that here: (1) What is A Notice of Intent to Lien And Should I Send One?; and (2) Construction Demand Letters – How To Write One That Gets You Paid.
For more information on pursuing mechanics lien claims in Louisiana: