psychometric function fitting with lmer?

I would think that the means of the group*cue effects are your bias parameters and the interactions with SOA are the effects on variance.

I don't this this follows because changes in both bias and variability
will (as I understand it) affect the intercept on the probit scale, so
only if you found no support for interactions with SOA (and therefore
no differences between groups/conditions in variability) could you
then unambiguously attribute the main effects to a change in bias.
Even then, your test of bias is surely underpowered since the effects
combine random variation in bias with random variation in the
variability parameter.