To mark all notifications, including Inbox notifications, as read in Liscio:
Select Notifications on the left-hand menu.
At the top of the preview box, click Mark All As Read.
Using the Mark All As Read option from your Notifications Center will also mark everything in your Inbox as read. If your Notifications shows 0 but you have unread items in your Inbox, it will mark the items in your Inbox as read.