Peter,
Yes 3dLME is hard coded with "Subj" as the default random-effects factor. So you may have to pretend that your 'Session' is your 'Subj' if you want to only model the random effects of "Session".
When you say that you want to model "monkey" as a fixed-effects factor, are you really interested in the differences among the three monkeys? If not, you don't have to explicitly put "monkey" in the model; that way the data from the three monkeys would be treated as three samples.
Gang