Step1: ensure that the both Line views do exist directly in the Application component. This only guarantees that the lines can be visible even if other components (e.g. Dialogs) are presented.
Step 2-A: If you are working with EmWi 9.30 or newer, configure the StackingPriority of the both Line views. Per default all views have the StackingPriority = 0. Thus changing it to a higher value (e.g. 1) will instruct the Mosaic to not display any other view above the both lines. See also: Control the stacking priority of nested views.
Step 2-B: If you are working with a version 9.20 or older, the implementation will be more complicated. Generally your would need to override the methods Add(), AddBehind(), Restack(), RestackBack(), RestackBehind() and RestackTop() the application component inherits from its base class Core::Group. Within the overridden methods you would then need to always rearrange the line views so they appear above other views. Don't forget to invoke the inherited version of the method (see super()).
Step 2-C: If you are working with a version 9.20 or older, and you don't want to override the above listed methods, the unique possibility is to structure your application in two main components A and B. The first component A will then be used to display all the contents of your application. It takes over the role of the Application component. The second component B will display only the lines. Within the application you arrange A and B so that B overlays A. Now, when you present a dialog in component A, the contets from B are not overlapped anymore.
I hope, it helps you further.