High lather is relative. You are asking one of the number one soap dilemas. High lather oils like coconut, are naturally higher cleansing. This is due to the high lauric and myristiric acids. There was a thread about this not that long ago I think.
Most people are going to tell you to get big frothy bubbles, you need either coconut, bababsu, or palm kernal oil. These are all higher in the "cleansing" fatty acids.
To get stable later, choose castor oil, this oil does not contribute to the cleasing quality of a soap.
Lard, palm and tallow have a creamy lather that also is low in cleansing.