Seems a simple thing really, but is it unusual that I just can't seem to crop well in Lightroom? I love it for organising and editing my photos, but I find that if I want to get fine grain cropping for screen or printing then I'm exporting the photo from Lightroom and then opening that up in Photoshop Elements and using the crop tool there as it's easy to set the size and aspect ratio you desire and then drag onto the image. I'm I just not finding this functionality inside of Lightroom, or does it really not exist and you have to use another application for that?
Lightroom gives some good cropping tools, IMO. Press "R" or go to the Develop module and click the crop tool below the histogram (though it sounds like you know that part).
To set the aspect ratio, in the Crop & Straighten tool area is an "Aspect" row, and from a drop-down you can select predefined aspect ratios, create a custom aspect ratio, or just freely crop it without restriction.
You can't crop to a size in Lightroom. When exporting you can specify the size of the image. So: crop to the aspect ratio you want (or to the width/height you want), then when exporting just be sure to enter the size you want to export the image at.
There actually is a pretty easy way to crop to a specific set of pixel dimensions in Lightroom, or at least to get extremely close to the pixel dimensions that you want - I've been doing it this way for years and it works very well in preparing my photos for printing.
Using Lightroom Classic (or Lightroom 6 or previous versions), set one of your Loupe Info overlays (found in Library > View > View Options) to include "cropped dimensions". Then in Develop module, click "i" to turn on the loupe info display (click it once or twice as needed to bring up the one that includes the cropped dimensions). Now use the crop tool to set your aspect ratio as you want, and go ahead and crop the image - you'll see the cropped dimensions change as you adjust the size of the crop or its aspect ratio. In other words you're getting a live read-out of the impact of your cropping in terms of pixel dimensions.
Sometimes it's hard to get the exact dimensions I'm after, but I can usually get within 5 or 10 pixels of my target - which is definitely close enough for pretty much anything I might want to do.
I haven't been able to find any way to see the cropped dimensions in Lightroom Mobile (cloud version) - if anyone does know a way I'd love to hear about it.