Sulfate FREE lather

If my shea moisture shampoo, and my organix coconut milk shampoo are sulfate free...why do they lather so well? Esp. the shea moisture?
I thought sulfates were what gives a product its lather?
thoughts?

Lather is a function of three key variables: the type of surfactant(s) used in the formula, the concentration at which they are used, and the presence of “anti-foam” agents. Anti-foamers are typically oily materials that “use up” some of the surfactants ability to produce lather.

The early sulfate free shampoos did not lather as well as their SLS based alternatives but the natural products industry addressed this and these days alternative surfactants are used to help the shampoo lather and cleanse
http://sulfatefreeshampoo.org/index.html