The general thrust of the comments is correct. The choice of MK or PK is make in the driver and it is almost entirely determined by the media type setting. If you choose one of the photo paper or proofing paper options you will get PK enforced by the driver. If you select one of the matte or fine art paper settings then MK will be enforced. Only plain paper allows you to choose the black ink, although MK is usually the default. You don't make the media option selection in either PS or LR - in either program you'll have to open 'print settings' and ensure that you've selected an appropriate media type. If you don't do this then you're playing Epson Roulette, in which some default option will determine the media type setting and hence the black ink. (I think that recent versions of PS will save the last used printer settings for some image formats like either TIFF or PSD. You can save combinations of settings, including the media type, as a preset in the driver, but you still have to open the driver options via print settings in order to select the preset.)