First thanks for all the comments and helpful advice so far. I already know what the print lab requires - sRGB and JPEG or Tif. I also know what there print resolution recommendations are...that is why I am asking about enlarging the photo. I'm sure it is not large enough as is.
I have more details and an experiment I did that maybe someone could comment on for me. The file was a raw file that I processed in LR4 and then took to PS CS5 for more editing, then returned it to LR4 as a tif file. The actual dimensions of the file are 2845x4286 pixels. At 300 ppi that will print 9.48" x 14.28". I want to print 16"x24". If I change the print size to 16x24 with resampling turned OFF in PS the resolution has to drop to 177 ppi. Not quite what is recommended by print lab.
I also realize that I can export from LR4 at any size I want. I just usually leave "Don't Enlarge" checked in the Image Sizing section of the LR4 Export dialogue box. Mainly because I have just never had a need to make an image bigger and I figured it would lower my quality.
Yesterday I exported the file at full size (no shrinking, no enlarging) at 300 ppi. Then I exported it again at 4200 x 7200 pixels also at 300 ppi. That is what is needed to print 16x24 at 300 ppi. When I zoomed in on both photos the same amount, meaning they filled the same amount of screen, I could tell no difference. Am I missing something here? Is it just because I am viewing them on a monitor and not printed that they look the same? If they truly are the same with no visible loss of quality then that is my answer for how to make the photo larger for 16x24 print. However, I am skeptical because I have heard that even if you enlarge in PS by resampling you should do it in small steps, i.e. 10% increase each time until you get where you need to be. This enlargement in LR4 Export is just one giant step. Yet the quality looks the same to me.
Any more comments about this new info would be greatly appreciated.