A photo that is 442x552 cannot possibly be printed at a reasonable quality level at 16x20 (in fact it won't even print well at 4x6). Which brings up the question, what is the size in pixels (height by width) of the cropped photo that you exported?

In the export dialog box, you would need to specify that you want 240 pixels per inch, you would want to specify a width and height of 16x20 inches, and unclick "don't enlarge". BUT ... if the original cropped photo was relatively small (please tell us the dimensions, as I asked in the first paragraph), it is unlikely you will ever get a quality print from a small original.

No you didn't misunderstand. I asked two distinct questions.

If you have a 3321x4152 image, then you can print at 16x20 at 207.6 ppi. This may be sufficient to get decent quality, as 16x20 would be viewed from a short distance, further away than you would view a 4x6. However, if you export the photo at 442x552, then you will get lousy quality. You have to export at the 3321x4152 size, or even larger if you want. You have to specify the width and height and ppi in the export dialog box, as I described above.

I then tried another export at 16 x 20 and 240 pixels per inch.  That didn't work, LR just went into an export mode for a long time.  I finallt cancelled the export.  I'm guessing that is not possible so LR didn't know what to do.

Of course Lightroom can do this export. I don't know why it took so long (about how long did it take before you cancelled?)

Now, will the 3312 x 4140 work or should I fine tune the export some more(207.5 pixels per inch)?

Didn't I answer this already?

There's no practical difference between 207 ppi and 207.5 ppi, no one will ever know the difference.