I was on hold for quite a while, but Liftmaster customer support answered my question quickly. For the KLIK3U-BK and the model of the openers we have installed (purple Learn button), the key was that there's a hidden button on the remote that you expose by sliding down a panel in front below the external buttons. Calling this the 'remote programming button':
Press and hold the remote programming button until the light on the remote comes on
Press the Learn button ... its little light will come on
Press the button on the remote that you want to program to activate this opener 3 times. The learn button's light goes out
That's it. Just test the opener button you programmed and it should work. Put the cover back in place and you're done!