So you have a water analysis for the bottled water? What pH are you giving beersmith to get an adjusted pH or even mineral composition? You have to have a starting point. No software can calculate a mash pH without knowing the water pH to begin with. It's about the buffering values of the grain bill against the starting water pH.
what percent lactic acid? Same volume of water you mention in the OP?
My IPA/APA grainbill is pretty similar to this grain bill, a little heavier on the munich and c malt which will give me a bit more buffering power than your grainbill from the darker malts. On a 9 gal, 11.25 lb grainbill I get a mash pH of 5.87 without adding any minerals or acid. My water pH is 6.9 so the grain bill alone knocks a point off the pH. My minerals get me to 5.66, so close to your mash estimated mash pH and I use 3 ml of 88% lactic acid to get to 5.42.
I haven't used the water analysis in BS2 because I have all my recipes in Brunwater for that purpose and have checked all the Brunwater numbers with a pH meter many times so I trust it implicitly.
If you have no water analysis for your tap or bottled water then my advice is to use distilled water which is a known entity and build it up from there. Otherwise you're just guessing and could end up with a worse mess than adding nothing.