Is it possible to install Android apps on mobile running Cyanogen OS? I have a doubt on Cyanogen OS.

Can I install Android apps (e.g. from Play Store) on mobile (e.g. Lenovo Zuk Z1) running Cyanogen OS?
Cyanogen OS (not to be confused with open source CyanogenMod; is built on Android) comes with Google Mobile Services (GMS) and for GMS to be shipped in a specific device the device must follow Compatibility Definition Document (CDD) as well as pass the compatibility test. Any device which follows the said document and passes the test can be claimed as Android compatible. To know what having an Android compatible device means, refer to the document Compatibility Program Overview.

So yes, you can install (non-device specific) apps from Google Play Store on your Cyanogen OS.