From what I understand, you do have WLM on your phone. It's built into your messaging hub. It's just not labeled as WLM.
If you click the Messaging tile, swipe right to "online."
Click the ... on the bottom right and choose the icon that looks like a person. This is that "status" icon. If you choose anything other than "offline", you'll be logged into WLM with the main LIVE account you used to set up your phone.
But this should NOT send invitations out to anyone. So I'm not sure what's causing that with your situation.