You became Tekken Lord in Offline Mode.
To become a Tekken Lord you have to fight ghosts, which to the game, means any CPU in Arcade or Ghost Battle. The Tekken Lord title is the fourth from last title you can achieve (The highest being "True Tekken God"). Along the way you will also get the Vanquisher title which means you are halfway done on your way to the Tekken Lord title.

Personally, It took me 377 W / 79 L to become a Tekken Lord.

If you are curious as to all the ranks you can attain, look no further:

Beginner
9th ~ 1st Kyu
1st ~ 3rd Dan
4th Dan: Disciple
5th Dan: Mentor
6th Dan: Master
7th Dan: Grand Master
8th Dan: Brawler
9th Dan: Marauder
10th Dan: Fighter
11th Dan: Berserker
12th Dan: Warrior
13th Dan: Avenger
14th Dan: Duelist
15th Dan: Pugilist
16th Dan: Vanquisher
17th Dan: Destroyer
18th Dan: Conqueror
19th Dan: Savior
20th Dan: Genbu
21th Dan: Byakko
22th Dan: Seiryu
23th Dan: Suzaku
24th Dan: Fujin
25th Dan: Raijin
26th Dan: Yaksa
27th Dan: Majin
28th Dan: Toshin
29th Dan: Emperor
30th Dan: Tekken Lord
31th Dan: Tekken Emperor
32th Dan: Tekken God
100th Dan: True Tekken God