Resizing for large prints?

Here's an article I wrote, "How Large Can I Print My Photo? Understanding, Displaying and Managing Print Resolution" that will give you some idea. Since the answer does come down to "it depends", ultimately a test print as JoeKostoss suggests is the best way to go.  This was written before the Preserve Details method of enlargement came out, so you may be able to push it further than I suggest .

If you have the CC Photography plan then you have access to PS. The latest 2018 version of PS has a new image resizing algorithm called Preserve Details 2.0. Here's a good article on using it to upscale your JPEG and retain maximum image detail:

Best Way To Enlarge Images In Photoshop CC 2018

One suggestion:

Import the up-sized image back into Lightroom

Set a square crop in the Develop Module

With that square, crop a small detailed section of the print

In the Library Module, check the size of the cropped image in pixels.

If the size is more than 800 pixels per side crop again to a smaller section until you get an image less than 800 pixels

Divide the pixel dimension by 180 to get a print size at 180 ppi.  Example 800/180 = 4.44 inches

Print that cropped image on a 5x7 or larger sheet of paper from the print module with the following changes:

     In the "Image Settings" panel uncheck "Zoom to Fill"

     In the "Layout" panel, check "Keep Square" and type in the result from your calculation above (Example 4.44).

Print that image on a 5x7 sheet or larger.  This will give you a visual of how the whole print will look. 

Hint:  Don't pixel peep, that is view this 5x7 from a distance that the viewer would normally see the full print, which would be about 3 x the diagonal, or about 10 feet for a 24 x36 print.

The file size of a jpg is not an indication of image quality - the file size depends largely on image content, and the degree of compression used when saving.

The important numbers are the pixel dimensions. To print a 24 x 36" image at 300 ppi, you need 7200 (24x300) x 10800 (36x300) pixels.

300 ppi is overkill for an image this size, so if you use 180 ppi, you will need 4320 x 6480 pixels.

If the image contains less pixels than this, it will need to be resampled, and there will be some quality loss.

My question is how distorted will my print be at this size?

View the image at 1:1 (100%), and it will give you a pretty good idea of how the image will print.

What are the pixel dimensions of the original image?

I suppose that depends a lot on how you resized the image. Whenever an image is artificially made larger by any software there is a risk of some distortion. But it will be difficult for anyone to accurately tell you how well the print will look. I have a terrible memory anymore, but somewhere I recall reading that looking at an image at 50% magnification will give you a reasonable idea of how well it will print. Take that bit of advice for what it cost you.