I have versions 2.3 - 5.6 of Lightroom on my computer. Can I delete any of these without jeopardizing the integrity of my current Lightroom 5.6?
You can delete all of them, except of course the Lightroom 5.6 installation.
Yes, they can be deleted. There is no interdependence between versions of Lightroom.
You can uninstall all except, 5.6 best to use your operating system normal uninstall process. This will just remove the software application and will not interfere with your Catalogs, Preferences and personal files. If you ever need to download any of the prior versions they are all available for download at the link below.