I understand that this can be done using the "curve fitting toolbox" which I dont have on my system.
That doesn't sound right. You might be thinking of LSQCURVEFIT in the Optimization Toolbox,
which does return Lagrange Multipliers, lambda, as an optional output argument. So, if you don't have the Curve Fitting Toolbox, but you do have the Optimization Toolbox, your problem could already be solved!
The rest of your question, I cannot understand, I'm afraid, in particular what your "third curve" refers to. You mean you want to fit a different curve to each isocontour and plot the associated Lagrange multipliers as a function of the isovalue?