My experience has been the same as Soapmaker's. Lavender EO caused all-over rancidity quicker than the mint for me -- maybe 1-2 months difference between the two. I stopped using lavender EO quite soon after realizing how very fast the soap became rancid with this EO, but I used mint EO several more times before I wised up to it. I didn't know at that time about ROE, or I probably would have tried that. Instead, I switched to only using FOs in soap partly due to this problem and partly due to cost.
I don't know the chemistry reasons behind this problem. I do remember reading an article by Robert Tisserand about oxidized lavender EO being a skin irritant. Lavender is normally thought to be pretty safe on skin, but once it become oxidized it can be an irritant.
I reasoned the oxidation might also be the reason why some soap scented with lavender does okay and some does not -- it might be the degree of oxidation of the EO that makes the difference. I don't know of any way outside a well equipped chem lab that we can tell the difference, unfortunately.
I now use ROE and a chelator in my soap and seldom have problems with rancidity, but I know these ingredients can only do so much. I still try to avoid things I know are troublemakers, and lavender and mint EOs are on my troublemaker list.