I'd bet more on the age of the soap having a lot to do with the improvement in lather quality.
Early on in my soaping misadventures, I made a high lard soap that didn't lather well after the usual 4-6 week cure. I was so frustrated! I stuck the bars in a dark corner and promptly forgot about them. About a year later, I rediscovered the bars and was ready to pitch them, but decided to use one to wash my hands just out of curiosity. It lathered really well. Lesson learned -- sometimes patience is the most valuable ingredient in a soap.