Quite by accident tonight I discovered a "hack". Enter an invalid password at the lock screen and it will stay there and not fade to black.
I'll be using this technique myself from now on until a better answer comes along. The duplicate candidates don't work for me under Ubuntu 16.04 and like yourself it irritates me the screen turns off.
Feb 20 2018 Update - Disable Dimming CLI method
To prevent screen from turning off you need two settings, one under battery power the other when plugged into wall outlet (A/C).
For battery timeout:
gsettings set org.gnome.settings-daemon.plugins.power sleep-inactive-battery-timeout <time_in_seconds>
For AC timeout:
gsettings set org.gnome.settings-daemon.plugins.power sleep-inactive-ac-timeout <time_in_seconds>
So for both Battery and A/C set the time to 0 (never).
For Login screen:
gsettings set org.gnome.desktop.screensaver idle-activation-enabled false
Disable dimming screen when idle:
In Unix & Linux someone complained when on battery screen dims every 20 seconds and wants to turn that feature off:
gsettings set org.gnome.settings-daemon.plugins.power idle-dim false