You first battle him right outside of cherrygrove city; he uses his newly stolen starter.
You next battle him in Azalea Town. He will have a lv. 14 Gastly, a lv. 16 Zubat, and his evolved starter.
Then you battle him at the burned tower in Eckruteak. He will have a newly caught Magnemite as well as the Gastly, Zubat, and of course his starter.
Next you battle him in the Goldenrod underground. His Zubat and Gastly will have evolved into Golbat and Haunter, and he will have a newly caught Sneasel.
Victory Road is the last time he challenges you before the Elite Four. His Magnemite will have evolved into Magneton, and he will have a newly caught Kadabra. His starter will be the final evolution.
Finally you battle him at Mt. Moon, in Kanto. His Kadabra and Haunter will have evolved into Alakazam and Gengar.
If you revisit the dragon's den in Blackthorn City, you will not battle against him but with him. A double battle will occur against Lance and Clair
Now, on Tuesdays and Thursdays you can find him in the Dragon's Den and battle him. On Monday's and Wednesday's you can battle him at the Pokemon League.
Hope this helps =)