A 20 x 30" print would be in the 3:2 aspect ratio, and shouldn't be cropped at all. However, a 16 x 20" print requires a 4:5 aspect ratio. So you would need to crop the image accordingly in Lightroom or Photoshop.
so when exporting a 20x30 through LR to local lab, under resize should I input 20 x30 in the w & L dimensions?
I would send the full-sized image. That gives the lab the maximum number of pixels and therefore would allow for the best quality possible. As far as a 16 x 20" print is concerned, I would provide as large of a file as possible. My experience with online labs is that you specify the actual size of the print on their website. You just need to provide an image large enough to support the size you are ordering.
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For very best quality, make sure you crop first to the correct aspect ratio as Jim notes. Then in export, set the size to your final size. You only really have to specify the long edge as the other edge will automatically follow and set your export resolution to 300 ppi. This will scale the image to the correct resolution and will largely avoid the lab's scaling which is generally lower quality than what Lightroom does. Also set your output sharpening to the type of paper (matte or glossy) and use at least medium sharpening. Lastly, in general export to sRGB jpegs of quality 80. Anything above is a waste of bytes as there is absolutely no way you can discern the difference but if it makes you feel better, use higher quality settings. Amazingly, if you print at sizes that are smaller than the native resolution of the file resulting in downscaling of the image in the export I describe, you'll actually get a sharper looking print than when you send the full resolution image. This is because the output sharpening, which compensates for the inherent smudging in the print process is applied at the correct resolution. If you apply the output sharpening on the native resolution in that case, you won't see much effect.
Lastly, if the lab offers it, to use their icc profiles for the paper/machine combination they'll be using. Many labs offer this.
The scaling and sharpening are by far the most important for final quality. This makes a real difference in perceived sharpness of your print. Secondary is using icc profiles for best color quality, but sRGB generally works very well except for really saturated colors and it might actually not be very useful if you have a standard monitor that is close to sRGB.