Lineage OS is a ‘bare bones’ system: it has the basic apps - phone, email, sms, browser, calendar, contacts - but not a lot else. It doesn’t even have a built-in app store: either you install a version of GApps with the play store built in, or you add a third-party store like F-Droid or Aurora. It’s great, but there’s a lot the user has to do - some of it quite technical - before their LOS device is ready for everyday use.
LOS also does not provide any infrastructure: you need to go elsewhere to find somewhere that gives you an email address, a platform to sync your files, pictures, music, contacts, calendar, to backup your phone…
Google gives you those things 'out of the box`, providing a complete solution for new user who may not have already have an email address. Just create a Google account, enter the account details in your phone, and you’re ready do to almost anything, with no further ‘fiddling’ to do.
/e/'s aim is to do that too: create an /e/ account, enter the account details in your phone… (It’s not quite there yet: backup and restore is a release or two away, some of the everyday stuff has bugs, but it’s not far off).
So going back to the original question, /e/ OS adds an awful lot of things: file, contacts and calendar sync, an app store, tasks, notes, email, launcher , weather app. Also the lower level stuff - that is present in Google but not in LOS - to make all those features work. All in all around 30 components that are not present in LOS.
.