Soaps with lanolin (or a lanolin derivative) include J&E Atkinsons I Coloniali, the Dovo soft soaps, Acca Kappa 1869 in the tub, Fiori i Frutta and Institut Karité. Don't know if the concentrations are higher or lower than MWF, though.
But since MWF (in the ingredients list) lists lanolin after the fragrance components, the concentration of lanolin in MWF shouldn't be very high.
Attention: you skin's reaction could be due to the lanolin. Or could be due to another component, e.g. from the fragrance.