My grandmother used to make what we called 'lye soap' and I think she mostly used it for laundry. When I would get poison ivy they would tell me to use the 'lye soap' and it would help dry it up faster. Then I grew up and realized that all soap is made with lye. Now I don't know if her 'lye soap' was any different than normal soap, but it sure seemed to be.
Yes, all soap is made with lye, so it's all technically "lye soap" but the reason your grandmother's soap worked to dry up poison ivy is because laundry soaps were (are) made with a zero to extremely low superfat. For soap to wash the skin you want one with a superfat so that it'll be gentle, but to get greasy dirt out of soiled clothes you want something very active. A zero superfat lye soap that will dissolve grease in the wash will strip all the oil off your skin and will help to remove the urushiol oil as well.