When a professional photographer sends over a file, exported by LR, I have a hard time accepting the fact that they send over (FOR EXAMPLE...remember these are examples I'm using) 3 separate files for each photo in order for their client to print 3 different sizes.
That is precisely what I do, UNLESS the recipient is an editor or art director who wants to crop the image to fit a page layout, in which case I send him the entire photo. If it is going to somebody in whom I have no confidence he will crop it properly, I do it.
Excuse me for being confused by the (loosly used) word "crop." I am relatively new to LR, as mentioned above, I typically use it for personal use. When I think "crop" I think of maybe... a cropping tool. Not the exporting process.
The word was not used loosely and you are right - the reference was to the cropping tool in the Develop module and your image should be cropped long before you ever get to the Export page. When you crop you determine a shape (an "aspect ratio") not a size. The size is determined later in the Export dialog. So if you crop your image to have a 4:5 shape, it will be appropriate for 8x10 paper, 12x15 paper or 16x20 paper. Since most printers (other than Epsons) want to be fed 300 ppi, the machine will want 2400x3000 pixels for an 8x10 print, 3600x4500 pixels for 12x15 and 4800x6000 for 16x20. The pixel dimensions are 300 times the paper size because we are talking about 300 ppi. This resizing can either be done by you in LR or, as dj_paige suggested, you can send the original pixels that came from the camera, after cropping, and leave it up to the recipient or his printer to worry about the resizing to 300 ppi. Personally, I think LR resizing and post-resizing sharpening are as good as and probably better than other software and I like to see the resized/sharpened image before sending it off, so I do it myself through LR's Export dialog. To make it convenient the dialog allows you to make the calculation in your head of how many pixels you will need ("Hm, I want an 8x10 and I know that 300 pixels per inch is best, so I'll type in 2400 pixels for the short side. Since I have already cropped to 4:5, the long side will have to come out 3000 pixels") Or you can let LR do the calculating by typing 8 inches short side and 300 ppi (print) resolution.
If you want to supply a variety of different image shapes to fit different papers, 3:4, 4:5 and 5:7 for instance, you will have to do the different crops in Develop and they can be saved as Virtual Copies and exported as separate image files.
If a photographer came to me after doing my photos and said, "Hey, I'm going to need to know exactly which photos you plan on printing in the following sizes before you get any digital prints...." I would be a little shocked. Or maybe they would. In which case, I would not be returning to them....
But that is exactly what a photographer does. He says, "I supply prints in sizes x, y and z. Let's figure out how many of each you need." Or if he does not provide prints, but merely a disk, he will put the full variety on the disk. I wouldn't think much of a photographer who simply gave his clients out-of-camera shots and said to them, "Go bust your heads figuring out how to print them and if the store cuts off the top of somebody's head, that's your problem." If, however, you are o.k. with relinquishing control over your product, don't crop, don't resize, don't check that check-box and forget about ppi. And with so little self-regard you probably could have just shot jpgs and let the camera process them, and then you wouldn't need LR at all.