The Lykhosidae was not a Phoenix Lord, but rather an extended defensive system of Kaelor's infinity circuit. It was, essentially, an actual Warp Spider which hijacked the body of an Eldar to cure a physical corruption, instead of the usual psychic corruption the Warp Spiders deal with. Eldar Prophesy is actually a rather interesting book which adds far more depth to the Eldar as aliens than the Path books do. In the Path books, Eldar are just highly advanced humans with pointy ears.
But i digress... There is, to the best of my knowledge, no information on the Phoenix Lords of either the Shining Spears, or the Warp Spiders. There was a rumour that Nadau Fireheart was going to be re-envisioned as the Phoenix Lord of the Shining Spears, but as yet that has not been confirmed.
They generally both fall into the same category of the 2 missing Legions. They were initially created to allow people to 'create their own'. Since that practice has fallen onto dark times, however, we await the gap being filled... Which it probably wont.