Lightroom mobile is designed to be used on mobile devices like iPhone.
You cannot install Lightroom mobile on you Macbook Air laptop.
If you wish to transfer the images and the catalog to another machine, kindly follow the below link.
If you wish to use the same catalog on multiple machines, you may use a external hard drive to store images and the catalog. You would only need to connect it to the machine you are using and launch Lightroom using the catalog from it.
Hope this helps.
Thank you for your response,
With the help of support, I just downloaded and I have installed Lightroom in my McBook Air wich runs on OS X version 10.9.5.
I just want to know how to sync with my Main PC and I phone.
You can only synchronize one catalog's collection to Lightroom mobile (e.g. iPhone).
If you wish to sync your iPhone with the catalog on the MacBook Air computer, you need to enable the Sync with Lightroom mobile.
Note: This will remove any data you have from any other catalog from Lightroom mobile.
Hope this helps.
to make it abundantly clear, Lightroom cannot sync between two desktop computers. It can only sync between a single computer and one or more mobile devices. Syncing between computers has been a much requested feature but Adobe hasn't given us it yet. You'll have to designate one of your computers as your main editing machine and sync from there. There are tricks to get all edits from one computer on another one to be in sync, but these are not trivial and can lead to catalog corruption if you're not careful.
Thank You very much for answering the question and the clear response
Thank you for your response !