I remember 'James Brown Is Dead' when it was released in '91. It was definitely not underground. It was a major dance hit of the time, making into the US market, and being played on Video Hits etc. in Australia. It was definitely released by L.A. Style (Wessel van Diepen & Michiel van der Kuy). I can't find any reference to Lords of Acid being responsible for that track. I know a few tracks of LoA, and they're very different in style.
It's still interesting to know the track appeared in Apidya though. I can't remember the game. Maybe I missed that one.
edit- According to
Wikipedia , Apidya was released in 1992, so LA Style probably wrote the track first. Interestingly, both Chris Hülsbeck and LA Style released tracks on XYZ records. Also,
this forum post seems to mention the use of the James Brown is Dead track in Apidya, though I can't read German.