  For countably infinite IFSs on $\mathbb R^2$ consisting of affine
contractions with diagonal linear parts, we give conditions under which the
affinity dimension is an upper bound for the Hausdorff dimension and a lower
bound for the lower box-counting dimension. Moreover, we identify a family of
countably infinite IFSs for which the Hausdorff and affinity dimension are
equal, and which have full dimension spectrum. The corresponding self-affine
sets are related to restricted digit sets for signed L\"uroth expansions.
