First, locate the peaks using findpeaks or islocalmax to get the peak values (amplitudes) and locations. The findpeaks function also has an option to estimate the widths, and to get FWHM, use the name-value pair 'WidthReference','halfheight' (islocalmax does not have a similar option). Then as far as the fitting goes, iterate over the peakss in a loop to fit each one. I posted a similar solution in How to Extract/Fit bell curves under a time series... and while I can’t find an implementation of the Lorenz distribution, the File Exchange has the cauchy function (that appears to be well-regarded, although I’ve never had the occasion to need it so I have no experience with it).
If your spectrum nas baseline variation you want to eliminate, there are ways to do that as well.
