I am a Restoration company. We did mitigation work on a residential job. The house is owned by one person and I have a signed Service Authorization with her signature.
Whether or not lien rights will be available depends on the specific work being done. Because "water mitigation" can describe a wide array of activities, it's hard to provide a clear and concise answer.
Generally speaking, lien rights are only available to the extent that work was done which permanently affects the project property. And, that work that's done must generally physically alter the property or building where it's done. So, things like removing furniture or basic cleaning generally won't give rise to lien rights. But, if the work is repairing and altering the building itself (like the walls, floors, foundation, ceiling, roof, etc.), then lien rights may well be available.
Finally, note that a residential project could have some additional contractual and notice requirements in order for lien rights to be preserved. Levelset discusses those here: Texas Homestead Lien Requirements.