When you crop an image you automatically make the image smaller because you are taking pixels away from the image. In Photoshop you could use the size option to upscale your image. In Lightroom you can export the image and specify how large you want the exported file to be. In either case the programs are adding pixels to the image. Both Lightroom and Photoshop do a pretty good job of upsizing. But it's something you'll just have to experiment with until you understand what you need to do to get the size you're after.
When I crop an image in LR5, it severely cuts the file size down so that my clients aren't able to print their images in larger sizes. Is there some way I can prevent that, like when I crop in PS?
In my opinion, it is not the file size that makes the photo unprintable, it is the cropping or exporting settings that makes the photo unprintable. Are you doing a huge amount of cropping? Are you resizing at export? Please give us the details. Please tell us the size of the exported photo in pixels (height and width). Please tell us how large (what size paper) is the print going to be.
The file size is a relatively meaningless piece of information, and you would be wise to ignore it. It is more likely your actions (either cropping or resizing at export) that is causing the problem of the photo being unprintable. I say, don't look at the file size, don't try to achieve a specific file size, don't try to determine how to make the file size bigger ... instead make sure you are using the right export settings and crop size.
Okay, I think I'm getting it now. When I uploaded photos to print for clients, occasionally I would get a warning saying I didn't have a file size large enough for whatever enlargement I was wanting. To test what you guys said, I just did a crop in LR and it went from 6mb (4245 × 2830) to 2.5mb (3137 × 2091) and it was still large enough to print a 20x30. But when I export to 1200 pixels for the long side, and uploaded it to my lab, it gave me that warning. I guess I always assumed that it was the file size and not the pixels. I was always concerned that I would crop an image and it wouldn't be large enough for my client to have it printed as big as they would want it. When I edit, my workflow is to go through each photo, adjust and move on to the next~ when I am finished, I highlight them all and do a mass export, so it would be really difficult to go back through and figure out which ones I had cropped and export those ones separately. But now I know that it is possible to do what PS does in LR, so thank you guys!!
Are you sure the error message says file size?