I think I figured this out, but perhaps I don't fully understand what you want.
I think my issue was because I came from version 4 which had an option to pick transparent. Version 5, you can't. But you can uncheck "show notification icon". My setting must have been carried over/grandfathered over.
This does exactly what is says for main Tasker Profile notification. The notification is present, but you will not see this in your status bar (icon), only the notification shade.
NOW, if you want Tasker to not show ANYTHING on your lock screen, then that's controlled through Android notification, not Tasker. Android -> Settings -> Notifications -> Tasker -> On Lock Screen=Don't show notifications at all. You can also get to this screen by swiping the main tasker notification and clicking the gear symbol/more-settings.
Lastly, if you want to hide the icon for OTHER tasker/notification/"Notify"/task, Set the priority to 1 on THAT notify and it will not show an icon (regardless of if you pick one or not) on the status bar, but it will still be in the notification shade.
For some reason Tasker does not apply the main no-icon-rule-setting to sub tasks, but I think that's by design.