So can get rid of the “lock screen” (the one before we see the login prompt)? Turns out we can:
gpedit.msc as administrative user, then go to:
Computer Configuration ->
Administrative Templates ->
Control Panel ->
Personalization in the left pane and from there double-click the setting “Do not display the lock screen” and set the policy to “Enabled”.
The description with screenshots can also be found here.