There's a Lain one-shot ("Nightmare of Fabrication") that was included in the artbook; not sure if it was ever a doujin, properly speaking.
ANN credits him as the "original creator" as well as the character designer, and his interviews alongside Yasuyuki Ueda (who he also worked with on Haibane and Texhnolyze) seem to suggest that the two of them bounced ideas for the show back and forth during its creation.