4. After he lost to Red (aka YOU), he become the successor of Giovanni as the next viridian City Gym-leader and the only Gym-Leader who is not specifically using one Pokemon Type. This makes him also to the strongest Gym-Leader canonwise, even stronger than the elite 4 (bewcause he beat them all before)!
The Elite Four changed.
He's still stronger than them in GSC.
when and where?
I don't think he ever got a rematch. It actually seems that the only reason why Lance is Champion is because red was tired, or thought to be not ready, or whatever reason, being "strapped" on a throne as champ, where he needs to battle everyone who challenges him. It actually seems that he wanted to become stronger and stronger, train in a place where most people could not reach him, under extreme circumstances, not even visting his mother anymore, in order to become the ultimate Trainer.
It seems that the League needed a new champion, and the reason why it isn't blue could be 1. He already got the Gym Leader title and was happy enough with it or thinks that there is a greater chance to fight against other trainers thqn being champ (because the chance of beating the elite 4 is lower than defeating the other gyms, so there is a bigger chance to fight others while still fighting officially for the League) or, which is more likely, 2. He didn't see a point in taking the spot without "earning" it by beating the current Champion, which would actually mean that he is just a "false" Champ, only taking the spot because the other is gone. So Lance was just a fill in because they had nothing else to offer. Maybe they actually wanted that blue fights with lance to earn the title, however, Blue already beat Lance before and lance is not even the real champ, so, again, seeing no point in that.
____________________________________________________ "KILL ME! LEAVE ME TO DIE IN A POOL OF MY OWN BLOOD!"" - Mitsunari Ishida, Sengoku Basara 3
Huh wow I wonder why the changed that, and it's a shame they did seeing as we didn't get to battle a professor until Sycamore. I hope Sycamore remains a reoccuring character we can battle in the next version it's so fun to fight him. Though if you consider Coloress a pokemon professor he would be our first pokemon professor battle.
I've got a quote that embodies you perfectly, but it's seventy-three posts long, has a few massive flowcharts, and lots of Xion-KMA to Me