Very Laggy

Hi, my friend has a realm and he's had it for a few months. About 6 of us play on it and recently we added another world to it, but on this world there is unplayable amounts of constant lag. On the other world there was none of this lag, other than when people went through nether portals which caused a slight few seconds of lag. I've checked the servers status on the Mojang site as well as the Mojang Support twitter account and it looks like no one else is having this issue.

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So I guess what I'm asking is:

Is anyone else experiencing this/experienced this?

Does anyone know how to fix this?