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The isospectral deformations of the Frobenius-Stickelberger-Thiele (FST)polynomials introduced in [32](Spiridonov et al. Commun. Math. Phys.272:139--165, 2007 ) are studied. For a specific choice of the deformation ofthe spectral measure, one is led to an integrable lattice (FST lattice), whichis indeed an isospectral flow connected with a generalized eigenvalue problem.In the second part of the paper the spectral problem used previously in thestudy of the modified Camassa-Holm (mCH) peakon lattice is interpreted in termsof the FST polynomials together with the associated FST polynomials, resultingin a map from the mCH peakon lattice to a negative flow of the finite FSTlattice. Furthermore, it is pointed out that the degenerate case of the finiteFST lattice unexpectedly maps to the interlacing peakon ODE system associatedwith the two-component mCH equation studied in [17](Chang et al. Adv. Math.299:1--35, 2016).

Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials