You don't need two accounts, but you would need the account that you use on your MacBook Air to be your Primary Account as this includes Lightroom Desktop and Lightroom Mobile (a Lightroom Mobile only subscription doesn't include Desktop).
Also, with the Primary Account, how much Cloud Storage do you have? 1TB or 20GB? The lower amount may not be enough to accommodate what you may be using in Lightroom Mobile, which can be up to 100GB.
If storage is not an issue you can try this.....
- Create Album on Primary account.
- Enable Sharing for that Album.
- Invite email associated to your Mobile account.
- Ensure you give the Mobile account Can Contribute rights.
- Accept invite associated with Mobile account and sign in to Mobile account.
- Add Photos to Album shared from Primary account.
This will transfer photos over including edits.
You could transfer all photos to that Album and sort them from there, however it maybe easier to mirror your Albums in the new account and share each one (although you will have to accept an email for each album).