  We consider the multifractal analysis for Birkhoff averages of continuous
potentials on a class of non-conformal repellers corresponding to the
self-affine limit sets studied by Lalley and Gatzouras. A conditional
variational principle is given for the Hausdorff dimension of the set of points
for which the Birkhoff averages converge to a given value. This extends a
result of Barral and Mensi to certain non-conformal maps with a measure
dependent Lyapunov exponent.
