The Lingo Mac app offers some offline support though you may need to update your settings and get things ready before you disconnect.
To get the best offline support in the Mac App:
Open the app preferences at Lingo > Preferences.
Check the "Auto download" option
Set a file size limit that accommodates your assets.
Any assets larger than the size entered will automatically be downloaded and remain downloaded even if you have Optimize storage enabled.
It is also important that you open the kits that you want to be available offline and give them time to sync and download files. Browse around to make sure your assets have the copy icon instead of the cloud before you disconnect.