I have read several threads here and elsewhere about ideal print resolution settings -- most of them about printing a single image from LR.
Since I do a low volume of compositing photos w. digital art, I prefer not to use LR.
Many of us that a print from LR do extensive work on our images in Photoshop, but still move back to LR for output. LR prints a layered PSD or tiff file perfectly ... in whatever state the file was in when last saved - identical to printing it from Photoshop.
the reason LR is nice is because it can be used much like a RIP in it's layout features. Print presets are fantastic ... I can open any image in my LR library, go the print module and in 2 clicks have a print headed to one of my two printers which includes paper size, path and type, profile, any borders or borderless, output sharpening settings and more. I have about 8 presets for each of my two printers, and those presets will include all the properies of your print dialog box. You click the preset you want, if you have a watermark or signature you may need to move it to a better location depending on the image aspect ratio, and you click the print one button. No dialog boxes.
I also prefer Lightrooms interface to work with RAW images instead of ACR, although it's not like ACR is horrible. I just let the printer driver handle the resizing. I don't change the files size at all and don't worry about the DPI or PPI stuff. Whatever the native size is determines whether I choose 360 or 720, if it's greater the 360 then I will choose 720 and make sure I use the finest detail setting in the dialog box. If it's less then 360 I input 360 and leave that option off. LR takes care of the rest including the resizing and output sharpening.
If you don't have LR you may still just want to send the file to the printer at it's native size and let the driver handle the resizing as part of the screening and dithering.