We're sorry about the trouble with Lightroom. Would you mind telling us if you have the subscription for the application through the Google play store or the Apple App store & not directly through Adobe? If yes, then the subscription is for the mobile version of the application only & cannot be used to activate the desktop version.
If you have the subscription directly through Adobe, please ensure you are signed in to both the applications (mobile & desktop) using the same ID.
Thanks for the info! Please sign out of the Creative Cloud desktop app after quiting all Adobe apps & then sign back in with the same ID as the one you're using on the mobile device. Also, what happens when you try editing the images on the desktop? Are you getting an error?