I'm using LineageOS without Play Store/Services and would like to dispel this myth. Here are just some of the third party applications I can install directly from the developer using adb, without going through a third party store: Signal, Firefox, NetGuard, NewPipe, Orgzly, OsmAnd, Tor Browser. Those pretty much cover all of my smartphone needs and more.
The national 2fa app. The app people use to send money to their friends, sometimes street vendors. Rideshare app.
TL;DR: no Google, most things work, but not necessarily smoothly. I've used it for a few years now.
[1] https://lineage.microg.org/ [2] https://f-droid.org/en/packages/com.github.yeriomin.yalpstor... [3] https://puri.sm/products/librem-5/
You can use F-Droid (https://f-droid.org/) in place of the Play Store.