I wouldn't use a stir plate either. Oxygenating may inhibit the lacto.
Oxygen doesn't bother the lacto. The stirring action will help bring nutrients to the cells and carry away byproducts, as well as keep heating even.
Warmer is better. I don't think there is much difference between 90-120F, so just keep it as warm as you can without significant fluctuation. Consistent temp (just like with yeast fermentation) is important.
Referring specifically to lacto buchneri which is the WY5335 strain mentioned in the OP, here is the source of my understanding. Paraphrasing from Wyeast's Jess Caudil and Solera Brewing's Jason Kahler presentation at NHC 2012 A Perspective on Brewing Berliner Weisse-style Beer.
@45:48 The presence of oxygen will slow down the growth of this bug (WY5335). That’s why we… well… that’s not 100% why we purge a tank with CO2 prior to adding the wort and only the lactobacillus. It doesn’t help it, having oxygen present doesn’t help it. It will grow in the presence of oxygen for sure. But the main reasoning behind not having oxygen in the wort with only lactobacillus is you still have a lot of sugars sitting there for days and they start to brown up if you have a lot of oxygen there and that makes the beer oxidized and brownish.
Jason goes on to say later in the presentation-
No, there is no oxygenation at all at any point in the production of the beer. Actually a lot of care was taken to avoid any air being introduced. We pitched much higher rates so the oxygen free environment wouldn’t be a big deal.
I don't mean to be argumentative Kyle, you have much more experience with sours and various lacto strains that I do. Not sure if the OP is going for a BW, I just wanted to clarify where I was coming from and what makes sense to me from sources that I trust. To your point about nutrients and byproducts, to address that I gently swirl my flasks once or twice a day to mix things up a bit. Regarding even temperature, my flasks are in a fermentation chamber at steady temperature rather that a warming pad or band. Any further comments or insight on this would be greatly appreciated.