When this happens it feels so unfair, because you either troll them back and get punished (worse for you than for the other guy), or you let it slide and play anyways with another champion and let that dick get away with it.
The solution is easy: Make a report button at the champion select, which also makes the following happen:
If you win that game, the one who trolled you gets 0LP (or if we're harsher he loses the LP that he would lose for dodging the game ), while the rest get normal amount.
If you lose that game the guy loses double the amount of LP he would have lost (so if he lost 20LP, he loses 40LP).
This will present the troller with option to waste his time and lose LP, or to dodge and lose LP - there is no way out of it. Knowing this the one who wants to ban your champion because he doesn't like it, will not resorst to such actions to begin with. Remember people do this just because they can get away with it.
Continuing now... if the guy accumulates a certain amount of such reports, he gets perma-banned for toxicity.
The system would only trigger if your team mate banned a champion that you selected and got reported.
If this doesn't hit live, we'll know that RIOT encourages this type of behaviour.
Now, addressing some of incoming comments: "Then just don't show the champion you want to play" - my answer is: "some people have champions name or something relating that champion in their summoner name."