I have to agree that peat moss is not really the best thing to use in a rock garden soil mix. But lime is probably only best used with those particular plants that do well with it. I would tend to go with just sand, gravel, and humus perhaps with some commercial potting soil tossed in.
What you want is excellent drainage. Plants that grow in places that are rocky (alpine, high desert, outcrops, etc.) do so with very little soil. I have never heard of peat moss being found in such places!!!

Here is a link that might be useful: rock garden soils

Thank you for your comment, terrestrial man. Can you tell me how you get the humus, or are you saying that you get the humus from the commercial potting soil?

The recommendation of peat is from the best selling author Dr. Hessayon in his book The Rock and Water Garden Expert. This is very confusing indeed.

Googling Dr. Hessayon, he seems to be an expert on everything...
Of course, no one can be that, and I suspect he just took advice he received without giving it much thought.

Ditto what Tman said. I strive for a neutral soil, knowing that my water is from alkaline aquifers, plus made even more alkaline by the city municipality. If you're luck enough to have well water, you might also take the pH of that into consideration.

The purpose of adding peat in the mix is not to lower pH, rather merely adding a source of organic material that is resistant to breakdown and just happens to be acidic.

Rick

"Can you tell me how you get the humus, or are you saying that you get the humus from the commercial potting soil? "
Check the link below for making your own.
Or you can check locally to see who carries Kellogg's GroMulch. Here is a product that may be useful.
N Rich Compost

If you go this route I would use is sparingly. Say
1 part sand: 2 parts gravel probably 6 mm sieved or less
(here is a link to illustrate Garden sieve )and 1/2 part humus.
Have you ever been in a habitat in which plants that are grown in "rock" gardens are found? If so, then you would see that many plants are growing in debris accumulations that pile up in cracks and fissures between boulders or upon mosses or other pioneering plants that made a foothold into the scree field or mountainous area.
One thing I do is simply use leaves of hardwood trees or shrubs or even maple leaves when they dry up during fall and drop off the trees. Collect those and crush them up and mix with some general purpose potting soil, moisten slightly, and bag up and store in a warm place and then air out after a few months. Add more leaves if necessary then. Or you can add leaves directly to your sand/gravel mix and use as is.

Here is a link that might be useful: How to make humus for soil mixes

Finally found the sieve system I wanted to link you to in my post above. check the link.

Here is a link that might be useful: soil sieve system