To understand if the proxy server will work, you need to understand how the game stores data.
Google has updated its billing systems significantly over the years. Modern apps use the Google Play Billing Library, which creates a secure handshake between the app, the device, and Google's servers. This handshake is encrypted and difficult to spoof with a simple proxy server.
Ideally rooted for 100% success, though some non-root methods exist.
Google has deprecated the old purchase API (V2/V3). The built-in proxy of Lucky Patcher largely fails against apps using Google Play Billing Library V4+.