The “replacement for Play Services” is MicroG, which does its magic with the rather ugly hack of certificate spoofing, and consequently no larger distribution wants to touch it so that the masses would be able to use it more easily. Mentioning MicroG can get you banned on LineageOS forums, not because the Lineage team thinks that MicroG is unwelcome competition, but rather because they don’t want Lineage to be identified with a project that takes that approach to getting around Google.

But Play Services and related libraries for analytics or ads have a documented API. Isn't it easier either to write an implementation of that API or put Play Services into a safe sandbox rather than find time to write or port thousands of apps (that would require millions of man-hours) you could take for free from Android ecosystem?

Also, there are open source apps like Calendar, Gallery, Camera or Music that don't have ads and don't need proprietary components that you could use for free.

There is microG, but last time I attempt using it I run into issues installing their base services on a modern Lineage OS. Some people are using it successfully. It's kinda a shot in the dark really.