whats the statutory authority is for late filed liens and the penalty for late extension?
If you file a mechanic's lien late, your could be in legal trouble. There is no statutory authority for late filing, or a set penalty for late extensions (although I am not really sure what you mean).
You really should retain a construction attorney to review and evaluate your legal position based on the contract and pertinent documents. The right to be entitled to file a mechanic's lien is set out in Texas Property Code Chapter 53, and you really need to make sure that if you file a lien, you have properly and appropriately done so.
Filing an invalid lien could subject you to liability under the Texas Fraudulent Lien Act, and you could be liable for statutory damages of $10,000, or actual damages, whichever is greater, plus attorney's fees. Facing such a claim would add insult to injury.
Good luck.