No support. I don't see any reason for this. They can be annoying but just ignore them. Server load has nothing to do with this and unless you have a potato, you shouldn't have any noticeable performance drop.~ Jacob, Prince of the Kingdom of Heaven ~
Idk why people got this idea that "pets = all lag", because it's not pets that cause server lag; it's the players. And it's not the pets that cause individual player lag; it's the other players.
If you want to fix lag:
1. Jagex has to improve their servers so that they don't start producing their own lag after merely 300 or so players are in a server that's capable of holding 2k players.
2. If your ISP provides you with a crappy internet connection, you can't exactly expect high quality connection now can you? If possible, change to a better connection/ISP, but if not, made-up solutions like this won't work.
3. You can temporarily fix lag by changing to a quieter world, and further by going to a quieter location where applicable.