How to perform the Lookup Multi-Touch gesture using Magic Mouse?
You need to use a third party utility such as MagicPrefs or BetterTouchTool. I've mainly used the former as I've always felt it a bit more straight-forward when you just want to set up some minor extra functionality, but it hasn't been updated in a very long time and it feels like it gets buggier and buggier with each new OS X release.

BTT is definitely the way to go at this point, it has seen continued development and is really user friendly these days, and it's just incredibly powerful, once you've fiddled with it a bit and started to build up muscle memory you can get the Magic Mouse to do everything the trackpad does and much more.

In BetterTouchTool, select your mouse, and in the dropdown for predefined actions, choose "Lookup Word Under Cursor".