There are people here much more adept at answering this than me, but there are several things that need clarifying:
1. In your example, upsizing from 40cm to 60cm at 180 ppi (from 240) does not require an up-res. Simply resize the image without the "resample image" box checked.
2. Going from 40cm to 60cm both at 240 does obviously does require up-sizing, but most people would say you do not need to do this. Printing at the native 180 would be ok.
"Capture" sharpening should be applied before you resize, as its name implies. "Output" sharpening is applied after you resize. I recommend the Schewe / Fraser book "Image Sharpening."
Since you have Lightroom, I'm not sure why you want to go through all this. You mentioned this was a NEF image which sounds like you are still working on a RAW image. I would close the document and print from Lightroom. Then you have two simple options. First, under "Guides" check the "show dimensions" box; under "Print Job" uncheck the "Print Resolution" box:
1. With paper size and the cell size the dimensions you want, see what the ppi is. As a general rule, if it is 180 or greater, print away.
2. If you want more, i.e. if the image needs to be upsized, then select/check the "Print Resolution" box and type in what you want.
Much simpler in Lightroom, and the output sharpening is applied on the fly based on your selections in "print sharpening."
Even if you need to go to Photoshop for some post-processing and create a TIFF or psd or something else, the workflow in Lightroom is preferred by many.
Dave