A:Answer Whichever system you choose to set as your "primary" unit, the other(s) which have your user profile on them as well will need to connect to the internet to see if the title can be played (meaning, it is only being played on one unit). My advice would be to set your Lite as the primary and a docked Switch as the secondary since the docked Switch at home should always have internet access. If the travel one has to check online to see if the title can be played, you will need to connect to a wifi hotspot to allow this.
As for gave saves, if you have Nintendo Online, all game saves are uploaded to the cloud (for games that are compatible with this. The upcoming Pokemon Sword/Shield for instance will not allow cloud saves). Once you decide to use the other system, go to data management, save data cloud and then download the latest save data to that console. For games which don't allow cloud saves, you need to have both systems next to each other and do a manual data transfer from one to the other.