Getting faster internet doesn't provide a better ping. (In a raw sense)
Also (although I wouldn't recommending testing with speedtest.net) should supply a ping test to the location of your game's servers for a more accurate representation.
You lag because your low speeds when someone else is using the same connection
Are you wireless?
If not what type of cable is it and what are it's specs? (Should be on the cord)
You can also throttle the other's connections users but i'm not sure how low the speeds would have to be and they still enjoy their side if thats any concern to you.
WTFast works similar to how Firechat works. But adds a Server Roadmap Optimization Riot's guide gives a good idea. Theres nothing really you can do too much to lower your ping directly.
Mostly you just have to throttle. But i'm sure they will notice the unpleasant experience.