  We study a natural class of invariant measures supported on the attractors of
a family of nonlinear, non-conformal iterated function systems introduced by
Falconer, Fraser and Lee. These are pushforward quasi-Bernoulli measures, a
class which includes the well-known class of Gibbs measures for H\"older
continuous potentials. We show that these measures are exact dimensional and
that their exact dimensions satisfy a Ledrappier-Young formula.
