I also suspect lavender contributes to DOS, and not just with soaps made with unsaturated fats.
I did a batch of lard and coconut oil soap with high superfat early this year. I divided the batch into halves at trace. One part was scented with peppermint EO, and the other was scented with lavender EO. I poured both halves into the same log mold with a center divider and CPOP'ed the mold. I cut, cured, and handled all of the bars in the same way.
The EOs are the ~only~ difference. The lavender bars have gotten uniform DOS and the peppermint bars have not. I didn't realize I was going to be doing an experiment on DOS, but the results from my unintentional experiment are striking.
Robert Tisserand reports that lavender EO oxidizes fairly quickly and some anecdotal reports of skin irritation from lavender may be from using lavender that is past its prime. The lavender I used in my soap was from a reputable source. It was about a year old, however, and I suspect that was the cause of the oxidation in the soap.
My conclusions are to be wary of lavender EO and also to remain wary of high superfat even when using saturated fats thought to be less prone to DOS.