Here is how I'd do it using a virtual copy of your "master" and two areas in LR.....Crop and Export.
After finding out what resolution, file type and color space the Printing Service wants (say..."we recommend 300ppi, jpg and sRGB"), open your final tweaked image in LR and create a virtual copy. You'll now work only on the virtual copy, leaving your "master final" untouched. Let's say you want an 12x14 print.
Start with the CROP TOOL in the develop module. In the crop tool, set your aspect ratio to custom>12x14. Adjust the crop area per your liking on your image.
Next, click on File>EXPORT to open the Export Window. In Export Location, I'd create a folder to hold my ready for printing files, Titled "Ready for Print Service Bureau". Then in File Naming, give this file a custom name, ie, "pretty picture 12x14". Then in File Settings, set Image Format to jpg and Color Space to sRGB. Then in Image Sizing, click on "Resize to Fit" and set Long edge to 14" and Resolution to 300 pixels per inch. Then in Sharpening, choose whatever is appropriate.
Click on Export. You'll now have the ready to send file in your "Ready for Print Service Bureau".
For your next print size, return to your "master final" file and create a new virtual copy and proceed through these same steps but cropping and "resizing to fit" to your new print size, whatever that might be. This takes much longer to explain than to actually do.