First off, Lumin and Azure are different things.
Lumin is from a company called “Magic Leap” who make a VR/AR experience suite geared towards the enterprise, Lumin OS being the OS it operates on.
Azure is from Microsoft and is a cloud computing service where you can rent compute/storage on the web in “the cloud”.
Neither are part of Unity. Azure has its own pricing as they’re selling you compute power on the web. Lumin has all sorts of caveats depending what aspects of the entire suite you’re trying to tap into. Where as Unity’s “free license” is just for developing and releasing using the Unity engine. Just because Unity is free for you, doesn’t mean any other resources are free. You still have to pay for other things you may desire to use like Photoshop, Azure, 3DS Max, and more. Often times these things have free alternatives like Gimp and Blender, other times not so much (it’s hard to find free cloud services out there that scale). Unity has no control over that since those things are not controlled by Unity… Unity is offering you the engine, not the other things. Just like if you wanted to get a programmer to help you, Unity doesn’t supply one… well they also don’t supply cloud computing, Photoshop, or the sort.
As for there being a result when you google “Lumin SDK” coming back as “Azure”… no idea. Usually the first result in google is an ad. Are you sure you’re not just seeing an ad? Just because some result came back for an arbitrary search doesn’t mean that thing is actually related to what you’re searching.
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Now Unity does offer “build support” when targeting “Lumin OS” which is what that checkbox when you go to install Unity via Unity Hub is about:
This is just offering you the ability to build to Lumin OS if you want it.
So when you say “External Tools pane in Preferences is spitting out a red warning exclamation mark at me that I don’t have it installed”, are you referring to this:

Cause if it is… well, you need to install the Lumin SDK. That “Lumin OS” support is just the build support… it doesn’t install the Lumin SDK, just the Unity resources that are needed to target said SDK. Lumin supports the SDK itself.
You should probably follow the tutorial from Magic Leap for working with Lumin:
https://developer.magicleap.com/en-us/learn/guides/get-started-developing-in-unity
Specfically the “prerequisites” part:
Those “Install Magic Leap Tools” likely being the SDK as well as any other tools that Magic Leap offers.
Note, you will need to get a Magic Leap ID and other things to be allowed access to the SDK (and is likely why Unity doesn’t auto install the SDK for you… the Magic Leap license probably doesn’t allow 3rd parties to redistribute the SDK and instead requires you to go to them for it.)
As for what may be required to get that Magic Leap ID… I’m not certain. I haven’t dug into the requirements nor know what conditions may make it free or not (or if it’s 100% free). That is up to Magic Leap and Unity has NOTHING to do with how Magic Leap offers access to its resources.
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And NONE of this has to do with Azure… I honestly don’t know how you connected these together aside from you saw Azure as the “first result” when you googled about Lumin. Which as I stated… the first link is usually an ad… note the bold “AD” next to it in this search: