Disable MacBook screen turn off at locked screen
There is a free and open-source tool named KeepingYouAwake that can be used as per your requirements. 

Having KeepingYouAwake activated will prevent the screen from turning off when lock screen mode is activated.

Download the latest version here.

or install it via cask: 

brew cask install keepingyouawake.


This utility will not harm your Mac because it is based on an official command-line tool by Apple. BUT I cannot guarantee anything, so use this tool AT YOUR OWN RISK.