Texas prescribes the vehicle storage lien process to the day. Miss a window and the fee recovery, the lien, and eventually the title application are all built on sand. Here is the sequence, statute by statute.
Day 0: the vehicle arrives
The clock starts when the vehicle storage facility takes custody. Log the date and time of receipt; every deadline below counts from a mailing or receipt date.
Day 5 (or day 14): first notice
Written notice to the registered owner and each lienholder is due by the 5th day after receipt for a Texas-registered vehicle, and by the 14th day for a vehicle registered out of state. Notice may not be sent earlier than 24 hours after the vehicle arrives. See Tex. Occ. Code §2303.151 and §2303.152. A late first notice also delays when daily storage charges may begin to accrue.
Day 15 to 21 after the first notice: second notice
If the vehicle is not claimed, a second notice is sent in the window that opens on the 15th day and closes on the 21st day after the first notice was mailed (§2303.152).
Day 30 after notice: lien and disposal eligibility
The storage lien process reaches disposal eligibility only after the 30 day period following the completed notice sequence (§2303.154). If the owner or lienholder claims the vehicle at any point, the process ends there and the paperwork trail is what proves your charges were lawful.
The proof matters as much as the dates
Notices go by certified mail, and the receipts and return cards become part of the title packet if the vehicle goes unclaimed. Keep every artifact with the vehicle file.