Hi Gilbert:
It's my understanding from taking
Geoff Lawton's
PDC that truly "acidic" rain is localized to certain areas due to several factors including localized pollution and where the water is coming from. I believe I remember him saying that the most acidic rain ever measured was in Vermont.
I did find this website that explains some of this in more detail
http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap13.html
13.3 EFFECTS OF ACID RAIN
Acid rain falling over most of the world has little environmental effect on the biosphere because it is rapidly neutralized after it falls. In particular, acid rain falling over the oceans is rapidly neutralized by the large supply of CO32- ions (chapter 6). Acid rain falling over regions with alkaline soils or rocks is quickly neutralized by reactions such as (R9) taking place once the acid has deposited to the surface. Only in continental areas with little acid-neutralizing capacity is the biosphere sensitive to acid rain. Over North America these areas include New England, eastern Canada, and mountainous regions, which have granitic bedrock and thin soils ( Figure 13-2 ).
As a person living in an arid region like you with alkaline soils, I think adding lime would exacerbate more than it would help. I guess the big question is what are you using the water from the asphalt shingle roof for? If for watering plants, no big deal - rainwater falls on roofs and flows into the soils all the time (and off asphalt roads, etc, etc). Healthy soils with abundant organic material will help to bind up toxins from the roof.
Now if you want potable water from an asphalt roof, I know of people who have painted a product called "elastomeric" onto their roofs - you can find food grade elastomeric. Here is a wonderful article
Brad Lancaster, author of "Rainwater Harvesting for Drylands and Beyond Vol 1-2" (really - all westerners
should own these
books) pulled together about different types of roofs and the quality of rainwater, etc.
http://www.harvestingrainwater.com/rainwater-harvesting-inforesources/suppliers/roof-catchment-and-cistern-system-materials-and-supplier/.
Another book that would probably be most interesting to you is
"Toolbox for Sustainable City Living: a Do-It-Ourselves Guide" by Scott Kellog and Stacey Pettigrew. (the link is to the entire book
online). I had the pleasure of hosting these folks when they came through Phoenix on their book tour - their work is IMPRESSIVE. Essentially they rehabilitated a brownfield into a productive landscape in Austin. There's a ton of stuff on bio-remediation in the book.