My export settings are at 100% but my photos aren't saving at the highest resolution

One tool that might help solve this:

In Lightroom Classic, open the Metadata panel and set it to EXIF as shown in the picture below.

You should see two fields.

Dimensions are the width and height in pixels as imported into Lightroom Classic. 

Cropped are the width and height in pixels after any cropping.

The Cropped value is Lightroom Classic sends to Photoshop. If Cropped says 4500 x 3200 for your image, then what was sent to Photoshop is correct, unless you didn’t intend to crop it that way.

In my example below, it wasn’t cropped, so Lightroom Classic sends the full original dimensions to Photoshop. 

One more thing: 4800 x 6000 px is an aspect ratio of 4 x 5, which is understandable if you’re going to make a print based on 4 x 5 such as an 8 x 10 or 16 x 20. But 4 x 5 is not the native aspect ratio of most cameras (unless it’s a 4 x 5 camera, of course), so if the image was shot with a common DSLR or pro mirrorless camera (aspect ratio 3 x 2) some cropping will be needed. 

If Lightroom Classic says the Cropped dimensions are 4500 x 3200, that does not match either of the standard aspect ratios above, so if those are the current dimensions you may want to review how it was cropped, and crop it to 4 x 5 so that it matches the proportions of the intended final print.

I checked the image size in photoshop and it said the image was around 4500x3200 pixels (give or take).  For the large scale print she wanted, I adjusted the image size in photoshop and sent her a 4800x6000 version of the photo. My question is, why am I even able to edit the photo to be a higher resolution? Why isn't it already exporting from lightroom in the highest possible quality if my export settings are telling it to do so?

By @MackenzieSloane

To really answer this question properly by accounting for what happened along the way, we need to know:

What was the original width and height of the file in pixels, before editing in Lightroom Classic? Was it 4500 x 3200 px out of the camera, or something else? (The Metadata panel should be able to tell you.)

Was the file cropped in Lightroom Classic? (The full resolution Lightroom Classic exports is after any cropping.)

In Photoshop, when you adjusted the image size, if you used the command Image > Image Size, was the Resample option enabled?

You could also consider using a third party plugin to create files at the desired size. One such plugin is ON1 Resize AI (I think included in ON1 PHOTO RAW 2025 but also as a separate App, ON1 Resize AI). It gives you more controll.

"For the large scale print she wanted, I adjusted the image size in photoshop and sent her a 4800x6000 version of the photo. My question is, why am I even able to edit the photo to be a higher resolution?"

You are fooling yourself and your client. If you use Photoshop to change a 4500 x 3200 pixels image to 6000 x 4800 pixels, then that is called 'interpolation'. Photoshop will simply 'invent' new pixels to do this. You need to check your export settings in Lightroom and export directly at 6000 x 4800 pixels. Until we know which version of Lightroom you are using (and the pixel size of the original image!), we cannot say how exactly you can do that, but 100% quality and 300 ppi have nothing to do with the pixel size of the exported image.

Are you talking about Lightroom (Lr icon) or Lightroom Classic (LrC icon)? What version NUMBER?

You want higher resolution? Meaning what? What large size does the client want to print it at (on paper this would be size in inches or centimeters, width x height)? Please be specific, saying the client wants "higher resolution" isn't specific.

Why isn't it already exporting from lightroom in the highest possible quality if my export settings are telling it to do so?

You keep jumping from resolution (number of pixels) to highest possible quality, these are not the same thing, what do you really want? What does your client really want? Setting highest image quality with quality slider does not affect resolution, it only affects the amount of JPG compression used when exporting. Setting the resolution to be a certain number does not affect the image quality that the JPG compression uses.