Firstly version? The current public release 2.0.5? 

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If we say, more precisely, getting output from OpenLP — not just live lyrics — onto the projection screen then there are a number of things to setup/do. These steps are done with OpenLP 2.0.5 and Mac OS X 10.11 (El Capitan).

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In Mac System Preferences | Mission Control make sure option 'Displays have separate Spaces' is unticked

[Particularly if connecting via HDMI] Make sure external projector is connected to powered on Mac before turning on projector.

Turn on projector (external display, I did all these steps connecting to a HDMI Full HD - 1920x1080 monitor with a MacBook Air, a projector will be same steps) you should see the Mac screen on both the MacBook and projector

In System Preferences | Displays in the Arrangement tab make sure Mirroring is not selected so you get the projector's full display. You will then have, essentially, two screens. One on your Mac and one on the external display.

In System Preferences | Displays in the Arrangement tab make sure the menu bar is on the MacBook screen, not the external display (projector).<br>

Only then start OpenLP

In OpenLP go to Preferences | General, Monitors section of dialog box

In the 'Select monitor for output display' drop-down list you should see 'Screen 1 (primary)' and 'Screen 2'. Screen 2 will be the projector, choose it. Click OK.

And you should see output for songs go to the projector screen when you choose a song/run a service and send the song to live output.

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Good luck!