We apply and illustrate the techniques of spectral networks in a large collection of A K-1 theories of class S, which we call “lifted A 1 theories.” Our construction makes contact with Fock and Goncharov’s work on higher Teichmüller theory. In particular, we show that the Darboux coordinates on moduli spaces of flat connections which come from certain special spectral networks coincide with the Fock–Goncharov coordinates. We show, moreover, how these techniques can be used to study the BPS spectra of lifted A 1 theories. In particular, we determine the spectrum generators for all the lifts of a simple superconformal field theory.