Just to separate the variables, use a different "Turn screen off when inactive for" time and "Lock screen after" time under "Brightness and Lock" under "System Setting".
Leave the system inactive.
The screen goes blank after the appropriate inactive period.
After the additional screen lock time (or immediately if it is set to "When Screen turns off"), the screen turns back on and stays on, forever.
However, just move the mouse and then the screen will blank after the appropriate inactive period, and this time, and subsequent times, it will stay off.
Now, unlock the computer, and this whole sequence will repeat.