If you have a valid subscription, or 7 day trial of Lightroom ensure you are signed-in with your Adobe ID (see image below) by hovering your mouse near the name plate (top left) in the LR desktop app. Once signed in you can use the pause/play button to turn sync on and off.
If you have been using LR Mobile on the iPad as a free app you may need to create new collections or start automatic sync for camera roll. Any new photos you capture with your iPad will then be sync’d automatically.
It is only possible to sync one desktop catalog but that catalog can be sync’d to any number of devices as long as you use the same Adobe ID (email & password)
Thanks a lot for your comment.
However, not sure if that is replying my question. I think I need to put it a different way and make it simpler.
Let's imagine I bought the same day an iPad and a Mac. I also bought a valid subscription to Adobe Lightroom and Adobe Lightroom Mobile.
I shot some pictures and I prefer to edit them on my iPad. To do so, I imported them directly to the iPad and skipped the import on my Mac. The question is :
By clicking as above " Sync with Lightroom Mobile", am I sure that it will sync my pictures already imported on my iPad directly to my Mac or, on the contrary, it will only sync the empty local catalog that I created on my mac and then erase the pictures imported on the iPad?
Thanks a lot
All photos on the iPad will not be sync'd to LR desktop. You need to put them in a collection in LR mobile and the collection photos will then download via Creative Cloud to LR desktop once you start sync or turn off pause.