I do not use Lightroom but I have a suggestion. Because your question did not yield any results, you might do better asking in the Special Interests > Visual Media > Digital Photography forum.
Although I do not expect that there would be a great difference between those two machines running that application, you should be able to find someone who can provide some insight into the actual performance you can expect.
Be careful though, this is a very subjective question. On that same forum, a user recently posted a fine video that compared the difference between major photo editing programs. The systematic project compared DPP, Aperture, Capture One, Lightroom and DxO. His results showed mixed performance and this comparison showed that Canon's DPP trailed the other software with especially sluggish operation.
I suggest caution because my experience with DPP is quite different. I do not uses the other programs but the newest version of DPP is quite snappy on my i7 2.3 Mac mini. When compared to this video, for my use with my hardware, DPP outperforms the other packages on the posters nMP. My older Canon DSLR produces smaller image files and I am not using dual 4K displays.
In a similar way, your question introduces so many variables that it is tough to guess the relative performance of those two machines. Your Mac mini has less memory, a more powerful CPU, and (I assume) a slower 5400 rpm HDD. The Macbook Air has twice as much memory(!), a slower i5 CPU, and blazing fast SSD storage.
Perhaps you have not found "an appropriate benchmark" because one does not exist! In your position, I would be inclined to add memory to the mini and put it to work but you are considering that Macbook for some reason. 8Gb or more of RAM and SSD storage would place your mini in another performance category completely. Do you require portability or some other feature that the Macbook provides?
