The Litchi Mission hub is a web based application. As such, it doesn't matter on which device the mission was created. You must log into your Litchi account on the Mission hub and you will see it when you select the Missions/Open button on the bottom left of the page.
Make sure that when you are in Litchi on your phone, that you are logged into to your Litchi account. Create a mission, save it, then after logging into the hub, you should have access to it using the instructions I've given above.
What you CANNOT do is expect to run Litchi on your iPhone AND your Android device. They must be purchases separately.