We introduce two isospectral deformations related to the Frobenius-Stickelberger-Thiele (FST) polynomials. On one hand, for a specific choice of the deformation of the spectral measure, one is led to an integrable lattice (FST lattice), which is indeed an isospectral flow connected with a generalized eigenvalue problem. On the other hand, the spectral problem pertainning to the modified Camassa-Holm (mCH) peakon lattice can be interpreted in terms of the FST polynomials together with the associated FST polynomials, resulting in a map from the mCH peakon lattice to a negative flow of the finite FST lattice.

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