Would absolutely appear the contractor is way past the dates to file a lien on the property. Just google Texas lien notice requirements.
That said, he may still file the lien and provide whatever documentation and dates he wants. Then there process to remove it - which will be frustrating but this appears to be an obvious fraud / failure to follow the required notice provisions.
May cost you a few hundred with a lawyer. Have your documents and dates in order. And I would just not have any contact with him from here out as it will likely produce nothing.
Added Note: Get a trusted pool professional / inspector out there to inspect the completed work. Two things here - gives you more documentation / leverage against the contractor if his work was subpar or not complete. Second, you will know now any Easter eggs he left for you to find on the project. Better now than later as those things do not age well.
"The absence of the word accountability is not the same as wanting no accountability" -unknown
"You can never go wrong by staying silent if there is nothing apt to say" -Walter Isaacson