can images be moved within lightroom mobile

If you mean you want to create a custom sort order, then yes you can do that. Open the album, then tap on the tri-dot icon top right, select the "Sort by...." drop down list, select "Custom Order", then tap on "Edit" (on iOS) or the pencil icon (on Android). That opens the reorder screen, press and hold on the individual images then drag and drop them into the desired order. Tap on "Done" when you've finished.

Note that once a Custom Order has been set it will sync to all your synced devices, but will only be seen in that order when you select the "Custom Order" sort order. Note also that if you share the album online, by default the album will be shown in that custom order (which cannot be changed by the viewer). You can, however, reset the custom order back to one of the "standard" orders should you want to have the shared album shown in a different order, but that resets the custom order throughout the system.