La. Code Civ. Proc. art. 1154
When issues not raised by the pleadings are tried by express or implied consent of the parties, they shall be treated in all respects as if they had been raised by the pleading. Such amendment of the pleadings as may be necessary to cause them to conform to the evidence and to raise these issues may be made upon motion of any party at any time, even after judgment; but failure to so amend does not affect the result of the trial of these issues. If evidence is objected to at the trial on the ground that it is not within the issues made by the pleadings, the court may allow the pleadings to be amended and shall do so freely when the presentation of the merits of the action will be subserved thereby, and the objecting party fails to satisfy the court that the admission of such evidence would prejudice him in maintaining his action or defense on the merits. The court may grant a continuance to enable the objecting party to meet such evidence.
La. C.P. § 1154