AndrewK does it crash or just hang with an infinite beachball?
If it's a full crash, you might experiment by switching to another user account on your machine and seeing if OpenLP will run. If so, then there's some kind of corruption either in your OpenLP preferences or databases. You could try deleting everything but your actual data folder (~/Library/Application Support/openlp), which would be:
~/Library/Caches/org.openlp.OpenLP
~/Library/Preferences/org.openlp.OpenLP.plist
~/Library/Saved Application State/org.openlp.OpenLP.savedState
(I'm assuming you have OpenLP data you'd rather preserve; if not, might as well go ahead and delete the data folder too.)
If it's a beachball hang, you could be hitting the LibreOffice bug that prevents OpenLP from launching if the "Impress on macOS" option is enabled in Presentations preferences. If this is the case, launch OpenLP from a terminal window using "open /Applications/OpenLP" and then disable that Impress preference.