In general, dpi is the conversion from pixel dimensions (image size) to inch dimensions (on paper... X number of pixels per inch determines inches of paper coverage).

When we resample an image, we can specify its new size dimensions, like say 1800x1200 pixels.

Or, we can specify its new printed size, like 6x4 inches at 300 dpi, which computes the same 1800x1200 pixel dimensions (6x300 = 1800, 4x300 = 1200).

Specifying both dpi and inches of print size normally does this resample computation (computes new size of resampled pixel dimensions - to fit that declared paper size).

But merely specifying only dpi (called scaling, to fit the paper inches) merely stores that number in the image file somewhere (and we might then see some new corresponding print size numbers in inches, but the pixels are unaffected, NOT resampled due to the number). Dpi serves no other purpose, or has no other effect, on digital camera images. Only important at the time of actually printing (and deciding paper size).

The Photoshop resample box allows either method.

I think you are saying Lightroom export does the second method, which merely saves a dpi number for future reference. Any dpi number has no effect on the image or pixels, until possibly the time you may be actually printing it, and decide paper size, when you will surely address it again then.