What computations of the Lotka function exist for publications in humanities meta-disciplines? Given Lotka's law's general applicability to publishing rates and bibliometrics; what computations of the Lotka function exist for the meta-disciplines in the humanities?  (Philosophy, History, Literary Criticism by language, Film criticism, Anthropology, History and Philosophy of Science / Science and Technology Studies)

I wish to test cultural assumptions ("work culture") about publication rates of sole authored papers against Lotka values to check managerial assumptions, and my own assumptions, about productivity levels and "workload".  Yet I have no adequate grounding to find computed Lotka functions for discipline.
There have been a few papers published in this space by bibliometricians/scientometricians already. Having said this, why would you need pre-configured values of lotka's law for certain sub-disciplines in the humanities? 

I would collect data (perhaps using Web of Science/Google Scholar/Wiley/Elsevier etc.) ; then do empirical testing with the generalized Lotka's law on particular sub-disciplines and then control against your cultural assumptions and other variables. This is because every discipline changes over time and a paper published on this in the 1970's may yield different results now with the same methodology. Most of my references cited below point this (or some variation of this) out as limitations of temporally specific computations of these laws.

Having said this, there are a few papers which might help you in this task if you haven't found them already:

This paper specifically looks at generalizing Lotka's Law in the humanities and formulates the same queries that I laid out earlier about it being spatio-temporal specific.

This paper is the Pao's modification to Lotka's law for humanities and has some empirical evaluations from certain humanities literature. 

This paper is an empirical modification of Pao's variation (see above) to Lotka's Law in certain humanities disciplines.

This is an editorial response to Lotka's law applicability in the humanities.

This is a general paper which looks at quantifying author productivity and impact specifically in the humanities. It is a very good read for approaches.

In other words, do some up-to-date empirical evaluation and then perhaps, run your study. The first could actually make for a fine empirical paper by itself in the scientometrics world. Pre-configured function values are like using empirical regression estimates ; they are fine and specific to that study but may not be generalizable across all studies.