I've got to admit I've never tried this, but I do have a couple of comments/suggestions for discussion only.
Which Lacto culture do you have? 'parently WYeast Lacto strain is hetero fermentive, meaning by itself it may not produce Lacto, 'specially without yeast to use up oxygen.
In the no boil I worry about the 'barf smell' bugs, which aint lacto. Its the stuff which grows before lacto kicks its butt.
You could boil as per usual, cool, pitch Lacto and let breed for a few days then pitch the yeast and as suggested leave until you like the flavour profile. if it aint souring quick enough put a brew belt on at like 30 degrees.
Personally Id just use a normal fermentor if only using lacto (unless brevis), its everywhere and were always keeping it in check with standard brewing hygiene.
But as well people have reported good results with the no boil method, and ive never tried it, so really my comments are academic. :beer: