Lazy sync is an experimental/advanced feature. It's not on by default because it can lead to more sync/merge issues. You can end up working with an older copy by editing before a sync happens, and it can lead to confusion.
That said, if you're comfortable dealing with sync/merge then it can be a nice option. Basically, all this does is unlock Strongbox's local working cache first, giving you very quick immediate access to your database. It then performs a sync, so you will be initially working with the last known version of your database (which may not be the latest), and then having the sync work in the background and getting any updates.
If you get any sync/merge errors you'll need to know how to manage them but mostly it works ok, especially for KeePass databases where there is a very good merge process.
It can also be handy for users who's source/remote isn't always available, you get to unlock your database immediately, let sync fail, but live with that, and when your remote/source database is available, e.g. on your home LAN, then allow Strongbox to do a sync.
To find Lazy Sync, long tap on your database and tap on Properties, then find Lazy Sync among the options. Only for none local databases.