In the Mac preferences there is, or was, a section to specify which app opened when something was detected by the OS like the insertion of a memory card that had images or music or whatever on it. Check those preferences and assign it to open LR.
The only settings in OS X I know of are either the one in Image Capture's settings (read my original question), or right clicking on a file to specify a software to (always) open that type of file with, which is not relevant to my issue.
I never heard of anything else - let me know if there is another setting I'm missing.
I am on an iMac running Yosemite. I have had LR 5 and now using LR CC. I have not experienced this problem with HD cards from my Nikon D7000. I have always had LR open before inserting the card rather than using capture to open LR. Does your system work when LR is already open?
In older versions of OS X there was a CD-DVD option which IIRC worked the same if you inserted a memory stick/card of some type. Here's a screen shot.
Not sure if that type of thing is still available in the newer versions as most Mac's don't come with CD/DVD drives anymore and whether Apple has made that decision for the user without user input. Like they do with a lot of things.