Someone told me we can't install Google apps after installing LineageOS and it doesn't support Google Play.
What is the truth behind this? Can I access Google Play in LineageOS?
LineageOS is Open Source OS. Google apps like Play Store, Gmail, Maps etc are proprietary Google products and cannot be bundled with LineageOS due to licencing issues.
However, you can always download these Google Apps Packages (Gapps) to run with LineageOS. These come in different flavors, starting with minimal Google services to full fledged suite of Google Apps . For more details see LineageOS Wiki. Related Which version of Gapps to install for Lineage?
So, LineageOS by itself does not have Google Play but by installing Gapps of your choice, you can have Google Play and other Google apps of your choice.