Will Lightroom run on a Surface pro 8?

It will run, but the question is how well. Looking at some reviews, the Surface Pro 8 will be sort of in the middle of the pack. It will run OK, but won’t be a top performer because the fastest processor in a Surface Pro 8 is an 11th generation Intel Core i7 with integrated graphics. Photographers interested in higher Lightroom performance in Windows might choose a current 12th generation Intel Core i9 processor with discrete graphics.

One review says the Surface Pro 8 will probably run hot with loud fans if the CPU and graphics are working hard. That is consistent with what we see with many very thin, light Intel-powered laptops and tablets. The problem is, Lightroom will often make the CPU and graphics work hard, so you’ll get that heat and fan noise. High heat may also cause the processor to slow down. To avoid that, you have to use a bigger, thicker PC laptop with better cooling; or a cooler-running, more power-efficient processor like the Apple M1.

If you are talking about Lightroom Classic (LrC icon), it probably does run. Here are the current Lightroom Classic system requirements, look it over and see if a Surface 8 meets these requirements: https://helpx.adobe.com/lightroom-classic/system-requirements.html

Is it a good laptop? I don't know, I never tried. Laptops often come with slower CPUs, so you might want to consider getting a faster CPU. 16GB RAM is enough for most Lightroom Classic tasks, rarely is RAM a bottleneck (NOTE: for other programs that you might use, you may indeed need more than 16GB)

If you are talking about Lightroom (the cloud-centric software, Lr icon), then the answer is: I don't have a clue as I don't use it. If you are talking about very old versions of Lightroom, then the answer is maybe and maybe not.