Cropping in LC

"To create a cropped full frame image that matches the dimensions of a APS-C frame image."

What is your objective in creating the APS-C crop factor image? Knowing that we can probably provide other suggestions.

There is a plugin called "Any Crop" by John Ellis that will allow cropping to a 'Relative Size, which is what you're trying to accomplish. For example Canon APS-C cameras have a 1.6 crop factor, which has a relative size of 1/1.6 = 62.5% compared to a full frame camera. Just keep in mind that the cropped image megapixels (mp) will also be reduced. For example using a Canon 5D MKII the full frame 5616 x 3744 image has 21 mp and the 1.6 crop 3510 x 2340 image 8.2 mp. This gives you a comparison of what the image shot with the same lens on an 8.2 mp crop factor camera would look like. Using the same lens on higher mp crop factor camera will produce better image quality compared to the 1.6 cropped full frame image. This is for both onscreen and print output.

http://www.johnrellis.com/lightroom/anycrop.htm

The only parameter Lightroom has for cropping is aspect ratio.

There is no way to do what you want, you can't even crop to specific pixel dimensions, although Lightroom will display the cropped pixel dimensions as metadata in Library after cropping.

Do you mean cropping an image taken on a full frame sensor and cropping that to the area a DX sensor would have seen? The way to do that would be to create a preset that is set to exactly that crop. It is possible to do so but you would have to edit the preset manually in a texteditor to get it precise.

Do you mean a specific size in dimensions of the image?