Step one is to make sure your monitor is correctly calibrated, If you haven't done this yet, then do it now!
If the printer has an ICC profile for their printer/paper, then download and install the appropriate profile for your requirements.
In Lightroom, you can select the "Soft Proofing" box in the toolbar to view the image as it would be printed (Make sure the correct ICC Profile is selected)
You can crop to the correct ratio in the develop module, then resize to the correct dimensions when exporting.