From what I can gather, it doesn't seem like Janick writes very many lyrics. On BNW, Bruce has talked about writing all the lyrics to Ghost of the Navigator and Out of the Silent Planet, whereas both of the other tracks written by Janick are credited as Gers/Harris. On D0D, Bruce wrote the lyrics for Montsegur, Steve for DoD, and I'm assuming they both wrote them for Gates of Tomorrow. A case might be made for Jan contributing lyrics to his two songs on AMOLAD, Pilgrim and Legacy, but they are again Gers/Harris tracks, so it can be reasonably assumed Steve did most of the lyric writing. TFF = Alchemist is clearly a Bruce lyric, and The Talisman could be both Steve and Janick. Same goes for the new album, in which all of his songs are Gers/Harris. Having watched the documentaries, it seems like Janick goes in with mostly fully-formed songs and then Steve arranges them a bit more and writes lyrics on top of them.
Adrian definitely writes lyrics from time to time, but not always. It seems like he's been writing less lyrics over the years, relying on Bruce and Steve to help out with the words so he can focus on the music, but there's really no way to tell. Generally, if a track is credited as Smith/Dickinson, it means Adrian wrote the music and Bruce wrote the lyrics.
Dave is often more obvious. I'm sorry to say, but he clearly writes lyrics because they are most often the most simplistic, occasionally sophomoric lyrics on an album. The Man Who Would Be King being a prime example, he writes lyrics the way Steve writes lyrics when he gets in a rut: come up with something that fits in a pre-conceived melody, whether it works or not (i.e. throwing in as many "justs" into as possible or using the same word to end two lines in a row).
He actually did write some of the lyrics to New Frontier, and Bruce "helped him out with some of them", if I recall correctly from some DOD-era interview.
