As far as I'm aware, the only thing in GMLive that can cause IDE lag is if your code is constantly throwing up errors and they are piling up in Output tab until they eventually "clog" it due to there being too many lines.
Other than that, neither the extension or the server perform any direct or indirect interactions with IDE - the server checks the requested files for changes and sends them to the game whenever it asks if there's anything new.
If you can get this to happen on a small project, feel free to email me a YYZ, and I'll see if I can reproduce this on my end.