How to

LUTs in Lightroom

Lightroom loads LUTs as profiles. You build the profile once in Camera Raw, then it lives in your Profile Browser.

Open any photo in Photoshop and run Filter → Camera Raw Filter.
In the Presets panel, hold Option (Mac) or Alt (Windows) and click the New Preset button, it turns into New Profile.
In the dialog, enable Color Lookup Table and load the .cube file. Name it and save.
Restart Lightroom and open the Profile Browser. The profile is there, with an Amount slider for intensity.

On your phone: profiles created this way sync through Creative Cloud, so they show up in Lightroom mobile's Profile Browser too.