  We show that the Mahler measure of every Borwein polynomial -- a polynomial
with coefficients in $ \{-1,0,1 \}$ having non-zero constant term -- can be
expressed as a maximal Lyapunov exponent of a matrix cocycle that arises in the
spectral theory of binary constant-length substitutions. In this way, Lehmer's
problem for height-one polynomials having minimal Mahler measure becomes
equivalent to a natural question from the spectral theory of binary
constant-length substitutions. This supports another connection between Mahler
measures and dynamics, beyond the well-known appearance of Mahler measures as
entropies in algebraic dynamics.
