To see your touring plans in the Lines app, open the Lines app and log in. Scroll down to the My Touring Plans section. The three nearest-in-the-future plans are displayed. Click on the touring plan you want to view.
Only three plans appear for easy reference on the main menu of the Lines app, but you can view any of your plans. To do that, either tap the gray "All Plans" button that is part of the My Touring Plans row, or tap on Touring Plans (under "Planning Tools") and then Personalized Plans.
If you would like to make a single plan easily accessible, you can "select" it by tapping "Select Plan" while viewing your plan in the Lines app. Then you can then tap "View Selected Touring Plan" from the main menu to access it quickly.