I don't believe you can install the play store itself, but Spotify should work. You would have to manually side load it, or install the yalp store which will manage fetching and updating play store apps for you.
LineageOS really should find a way of making Webview available for people who do not load Play/gapps - MicroG is the only way to run an up to date webview if gapps is not present.
There are also two versions of the "Aurora Store" in F-Droid. These require your Google account at startup, and they supposedly handle the split APKs.
Yalp does warn that using your own credentials is a violation of Google's terms of service. Because of this, I have never given these credentials to Aurora.
1. WebView comes pre-installed on LineageOS, irrespective of whether you install Gapps
2. WebView can be downloaded separately from the Play Store