I was wondering if it is possible to put Google Play on a Windows Lumia phone?
No. Its not possible, unless its totally wiping the phone and flashing onto it an android operating system.
Windows Phone and Windows 10 Mobile (which is the OS on Lumia Phones) are not android based Operating Systems, so no android apps can run on this platform.
For the Lumias, you have the Microsoft Store as the official apps and media distribution for the platform.
You can read this article for more clarity on the differences of the current mobile operating systems