Great reply, I can relate to what you suggest!
On your question: "Does the musician request a song, or does it just come of it's own?"
A musician is always busy with music, listening, studying, discussing it with others, playing, improvising or composing. One can therefore say that a musician is always tuned with mind, hart and body to music and its astral counterparts, like a radio tuned to a broadcast. It can therefore be stated that there is always some sort of hot link present. Also, musicians, especially composers, have a hunger for that next tune, so basically there is this implicit request present.
It is a two way scenario in my opinion.
One needs to practise in order to enable a composition to land, so what would you do when in spirit and you would like to "download" a tune into the material world, hehehe.
If this is always a conscious process of channelling, well I would like to think no. But there are relations present, always!
On your other question: "..... does the ego furnish or influence the lyrics?"
Yes. To stop the process of thought and association is not easy, also ones body poses certain limitations. I can't play continuous 1/64 triplets in a 120 BPM tempo for two hours if you know what I mean.
Also, inspiration usually does not provide me with a full tune. I usually have this snippet or two that kind-a pop up out of nowhere. These snippets have those "magical" qualities but from then on it is work work work.