I waited for ages for LR CC Mobile to download my photos to my new Android phone, because I thought that it would be nice to be able to show them to my friends.
This evening I tried to do that and failed:-
The first hurdle was having to enter a user name and password. This had no effect, because my phone had no signal, or wifi.
For more information refer:Adobe Lightroom for mobile FAQ
Lightroom sends the photos up to Adobe's servers, and then down to your mobile device(s) - not directly from one to the other(s). So you need to be online to get photos onto the device(s).
To show pictures offline, I find the best way is to have an extra synced collection containing the photos from all my synced collections (see All Synced Photos in the Library panel). On the mobile device, set this extra collection to Enable Offline Editing, and sync to it while you're online. This means you don't have to enable that setting for each collection, and you just need to check that this collection has finished syncing - you can then be sure all the others will be available offline too.