Azure Redis StackExchange.Redis ConnectionMultiplexer in ASP.net MVC

The docs are right in that you should have only one instance of ConnectionMultiplexer and reuse it. Don't create more than one, it is recommended that it will be shared and reused.

Now for the creation part, it shouldn't be in Controller or in Global.asax. Normally you should have your own RedisCacheClient class (maybe implementing some ICache interface) that uses a ConnectionMultiplexer private static instance inside and that's where your creation code should be - exactly as you wrote it in your question. The Lazy part will defer the creation of the ConnectionMultiplexer until the first time it is used.