WIth OpenLP running in Live mode, in OBS, add a Window Capture to the Sources. You will see the OpenLP display window in the list. It won't matter where that window is, that is, where OpenLP is projecting (screen 1, 2, 3...)
But you should always know where OpenLP will project - select the desired Screen in OpenLP Settings.
If you don't want to project, or even see, the OpenLP Live display, you can have it show on Screen 1, but set the location of X to minus (width-1). But I'm not sure why you would want that.