If you are exclusively using Lightroom on your mobile, you'll need to get your presets from the purchased zip file to your mobile. This is the same for any preset pack you may have installed in the past. The instructions are as follows.
(Assuming you've already downloaded Lightroom for mobile)
Unzip the download on your computer.
Open the For Mobile folder.
Inside are .DNG files, you will need to get these on to your mobile phone. I suggest AirDrop on a iPhone or Dropbox/email/file transfer on Android.
(sometimes DNG files display as blank in your iOS Camera Roll, ignore that)
Now import these DNG files in to your Lightroom.
To apply these presets to your own photos, you simply tap the three dots in the top right of the screen, and then copy the preset settings from the preferred DNG photo on to your own. (You can also save them as quick-access presets by clicking "Create Preset" and saving it to your own library)