We used a third-party service (not Levelset) to file a notice for us on a public university project in Louisiana. The third-party uses an inhouse machine that post marks the notices as they are printed. For this project, the third-party printed & postmarked the notice several days before our notice deadline, but the envelope was not accepted at the post office until several days after our deadline. The third-party has stated the date accepted at the post office does not make a difference, and that the third-party has no control over when the envelope is accepted at post office. This seems doubtful, though, as any party could post mark a letter on a specific date and then walk it in to the post office days later. At what point does Louisiana consider an envelope to have been mailed?
It sounds like you might be referring to a LA Notice of Nonpayment. In Louisiana, this notice doesn't necessarily need to be received before the deadline. However, for the notice requirement to be satisfied, the notice must be deposited in the mail prior to the deadline (pursuant to LA R.S. 38:2242(F)). As a result, I would say that the date the mail is actually deposited at the post office is highly relevant.
That section reads, in relevant part: "The return receipt indicating that certified mail was properly addressed to the last known address of the general contractor and the owner and deposited in the U.S. mail on or before seventy-five days from the last day of the month in which the material was delivered, regardless of whether the certified mail was actually delivered, refused, or unclaimed satisfies the notice provision hereof or no later than the statutory lien period, whichever comes first." (emphasis added).