First way to get it is to play the Chocobo's Hot and Cold game and earn 10,000 points and redeem the points for Robe Of Lords by talking to the Mene the moogle
The second way is to go through the Stellazzio: Zodiac Coins sidequest. Give the 12th coin to Queen Stella and you will recieve a Robe Of Lords as your reward
The third way is to beat Hades and gain access to the Legendary Synthesis Shop. You must have a White Robe, a Black Robe and 30,000 Gil to get a Robe Of Lords.
The fourth way is to steal using Zidane. Bosses like Ozma and Hades carry a Robe Of Lords. Equip Zidane's Master Thief ability, which can be learned from using Thief Gloves (which can be bought in Treno's Auction House) and Bandit ability, which could be learn from Mythril Dagger. Equip the N-Kai Armlet to ensure that Zidane has a good chance of stealing successfully.