Last year I did 3 batches of sour without adjustment to 4.5 post boil. This year I did 4 batches using adjustment to 4.5 post boil. Last year's beers were not gross. This year's aren't done yet obviously but from tasting the hydrometer samples they seem a lot cleaner. So far...
At this early stage of trial I am willing to commit to saying that adjusting to 4.5 is insurance. However, its not a substitute for ridding your process of oxygen. I still purge with CO2 every transfer and every time I open a fermentor to take a sample.
That purge is what's scaring me. If we transfer the wort after mash, short boil, pH adjustment into a carboy (with an auto siphon to avoid splashing) to pitch the lacto there will may be some O2 in the carboy. Maybe we should use a smaller (3gallon) carboy to leave little headspace? Fermenting in a corny sounds ideal but I'm not brewing at home where I'd have access to the keg & C02.
There are a lot of ways to make a sour beer. The need to pre-acidify and/or minimize oxygen depend on your specific process. Here's an overly simplified look at how oxygen affects the major players in a sour beer:
Spoilage/acetic bacteria - O2 typically increases activity
Lactobacillus - O2 does not significantly increase or decrease activity
Saccharomyces - O2 generally needed to promote yeast health
Brettanomyces - O2 increases production of acetic acid and ethyl acetate. May be desired in small amounts, but not generally in large amounts
So basically, you want to take a look at what critters are in play to determine how you want to handle oxygenation. If you're kettle souring, you definitely want to minimize O2 levels to the best extent you can to inhibit bacteria that can create off flavors. But if you're boiling before souring, that isn't necessarily a concern. Also, if you're souring post-boil, followed by (or along with) Saccharomyces only (i.e., no Brett), then oxygen isn't really an issue.
In other words, I wouldn't sweat the O2 in your case if you're boiling prior to souring and just using Sacc.