I can not to remove the lock screen on my P8 lite. I go to Settings>Screen lock & passwords>Password. There I can choose only pattern, PIN or Password, but I can not to tap on- NONE. Under that is sentence - Disabled by administrator, encryption policy or credential storage.
Do you by chance have more than one user account on the phone? If yes, this would make it not allow for the none option to be used. You would have to remove all other user account, leaving just one remaining one, to make it work.
Also, after doing my original suggestion, did you reboot the phone? It won't work if you don't.