why do the warp spiders alone of the aspects have no phoenix lord?
who founded their shrines without one?
did one exist and was then slain?

some ideas for a phoenix lord
standard PL rules plus

Anstazi Shar, the spider queen

vemon blades, the lord has power blades which are envemoned and allow him to reroll any failed to wound roll

twin spinneret rifles these count as an assualt 2 spinneret rifle

warp spider host, she carries with her many tiny warp spiders which hunt psyic entities , the any pskyer within 12" of the lord makes all psykic tests on 3D6

Not a bad idea, despite the rules probably needing to go in the House Rules board.

Warp Spiders are not the only aspect without a Pheonix lord, as the Shining Spears also lack one. Parhaps there was no 'singular' one founder of their shrines. Parhaps they were thought up by a collective group of Eldar? Perhaps the laser lance was developed and it was decided upon to give it to Jetbike riders. From there Eldar who excelled at it became the first Shining Spears!

Similarly, perhaps the warp jump generator was just a form of transport before the Eldar realized they could go to battle with it?

I have a simple reason as to why there arn't Phoenix Lords for the Spiders and Spears, and that is because they weren't a part of the earlier Eldar collection, they were both added with the blue Codex.

Sure, GW could have made two brand spanking new models, btu either they were too lazy or they just wanted to keep it simple at the six already known Lords.

The fluff for the Spiders specificaly mentions that they are based on a lifeform that inhabits an Eldar Craftworld. The fluff for the original Aspects founded by Asurmen state that the first Shrine was founded on a barren world that Asurmen's people settled, from this shrine the original 6 Aspects where developed.

It is further mentioned that the Phoenix Lords (with the eception of Karandras) where the first and greates students of Asurmen. I think we can safely assume that the later Aspects such as the Shining Spears and Warp Spiders where founded later, perhaps by Asurmen or more likely by the warriors of the Craftworlds in question. As such they don't have Phoenix Lords.

Simply put, spears and spider are the newest kinds of aspects, so the closest thing to a phoenix lord would be there exarches who in comparison would be like children to the exarches of the older aspects who take on the experances of war from there predesesors.