Your statement seems very strong. Is Mac OS X not based on Darwin? Are you defining "lineage" in some way to only mean licensing and exclude the shared ideas (a kernel manipulating files)? Thanks for the "carcinisation" link.
To be more precise: this simplified history suggests a shared "lineage" back to the original UNIXes of all of BSDs (and hence Darwin and OSX) and of the GNU/Linux and other OSes https://unix.stackexchange.com/a/3202
So, "zero shared lineage" seems like a very strong statement.
So, "zero shared lineage" seems like a very strong statement.