No, it doesn't have to be Palmolive. That was just an example.
Due to feedback from some people who've ended up really drying out their lips from using this treatment, I recommend trying a somewhat weaker soap first (Softsoap or a kid's type soap) and if that doesn't work, then try an ordinary dish washing soap. Try not to use an anti-bacterial soap for they can be a little too strong.
Don't make the mistake of doing the treatment 3 to 10 times before evaluating whether the first treatment worked. Some who did that really burned their lips.
Read some of the other posts in this winding thread for any other tips.