After the Gym Battle, enter the Tower of Mastery and you will now be allowed to go up the tower.Enter the room on the third floor and talk to the guy with purple hair to obtain TM47 Low Sweep.
Exit and head to the top floor to challenge Korrina. She will give you the Mega Ring and lend you the Lucario that is fond of you. Both Lucarios have a Lucarionite and are able to Mega Evolve. You will have a Mega Lucario vs. Mega Lucario battle.
Successor Korrina
For this battle, you will also be using a LV32 Lucario. As you select to attack, there will be an option to Mega Evolve Lucario before choosing an attack. Using Power-up Punch is the recommended move to use as it is supper effective against Lucario and it raises Lucario's attack.
She believes that the Lucario would want to go with you on your adventure and she will give it to you.
As you finish the battle, head to the right of the Pokemon Center and look for the Hiker that was once blocking the way. He is looking for something. Give the Intruiging Stone That Tierno found and the hiker will give you a Sun Stone. Exit to the right and your rival will give you HM03 Surf. Make sure you have an extra space in your party as you will recieve a Pokemon as you exit this city.