The way I interpret the question (and I also don't know LINCS data) is that gene expression levels are normalized to z-scores and the OP wants to summarize these gene expressions in each experiment by averaging the z-scores. Stouffer's method instead would combine p-values, which could be extracted from z-scores, to get an overall level of significance of the underlying tests.
E.g. if two genes have z = 2 and 4, the summarized expression would be 3. Instead Stouffer's method would give p = 0.999989 corresponding to z = 4.2.
If my interpretation is correct I don't see it wrong to average z-scores, or taking the median if one is worried about outliers.
Did you find the answer?
I have a same problem!
I have a similar problem but I am trying to replicate the conversion of Level 3 data to Level 4. Any idea how that can be done? I have used standard z-score, robust z-score (using median) but I can't seem to replicate the Level 4 gene expression values.