Lesson Schedules is not available at the stake level, but stake leaders and clerks have administrative rights for their own ward so that they can learn how the application works and provide training and support to ward administrators.
On the site here: https://www.lds.org/lesson/ I cannot see any administration options for my ward. However, for our Stake Executive Secretary on the same screen, there is an administration option. Attached is a screen shot of what I see.
Is this a bug? I know my calling in MLS is not set as a custom position since I have rights to everything else, such as handbook 1.