La. Stat. tit. 9 § 4204
If, in the agreement, provision is made for a method of naming or appointing an arbitrator or arbitrators or an umpire, this method shall be followed. If no method is provided or if a method is provided and a party thereto fails to avail himself of the method or if for any other reason there shall be a lapse in the naming of an arbitrator or arbitrators or an umpire, or in filling a vacancy, then, upon the application of either party to the controversy, the court aforesaid or the court in and for the parish in which the arbitration is to be held shall designate and appoint an arbitrator or arbitrators or umpire, as the case may require, who shall act under the agreement with the same force and effect as if he or they had been specifically named therein. Unless otherwise provided in the agreement, the arbitration shall be by a single arbitrator.
La. R.S. § 9:4204