I've done some more reading of natbib itself (the included pdf) -- it's pretty clear that if natbib is set to *author-year* style, then the standard \cite command behaves as \citet; if set to *numerical *style, \cite behaves as \citep.
You can see this in LyX when using natbib under Document -> Settings -> Bibliography: Citation style. If Natbib is chosen and set to author-year, the LyX source code shows citations as \citet; if you change that setting to numerical, the source code updates them to \citep. So I take this to mean that LyX is using \cite, err, 'internally', and the source output reflects the implementation in the natbib package. Is it possible to control this in LyX somehow; to tell LyX to issue \citep explicitly and never use \cite? Can a natbib .cfg or .sty file change the behaviour? (Maybe this is all really a question for the natbib community?) I feel like I must be missing something obvious.
