That did the trick! So you just need to configure "transparent" icon in the dropdown menu... Then it disappears from lockscreen, and also from statusbar, although you still can see Tasker in notifications panel. Exactly what I wanted it to be.
Thanks a tone Pent! :)
PD: May be you could change a bit the settings so it's more clear... May be just include a new setting "don't show icon in statusbar" or something like that...