It is certainly possible to install the Play Store and MicroG on LineageOS. I've written a guide on how to do it here: https://blog.LineageOS.one/how-to-install-play-store-on-lineageos/
There are a few things to keep in mind, though. First, you'll need to be running a recent version of LineageOS - currently, that's 15.1. Second, you'll need to use the official LineageOS build for your device. And third, you'll need to install the latest MicroG build that matches your LineageOS version.
Once you've done all that, you should be able to log in to the Play Store and use all of its features, including downloading and installing apps.
