I have had a few lessons w/ some of the big dogs - Oz Noy, Nir Felder, Byran Baker. For each of them, I told them exactly what I wanted to talk about when scheduling the lesson. I also made a set of notes/questions in case I got distracted during the lesson.
For Baker, he records the lesson video and sends it to you. I also took notes and recorded the audio. For Nir, he sends PDF's of the stuff you talked about. I also took lots of notes during the lesson. For Oz, I just took a lot of notes.
I played a bit for all of them but didn't send anything in advance. Somewhat related, I took correspondence lessons from Chris Crocco and did have to send full recordings before he accepted me as a student. The lessons were built around what he heard in my playing.
My experience has been really great. There were some freezing issues w/ Oz but I was using an older laptop at the time (2009). I had no issues w/ Nir and Baker. All of the guys were really open, cool as hell, and a lot of fun to talk with. They all played a lot while explaining the various things we talked about.
So my suggestion would be to think about specifically what you want to talk about - something in their playing that interests you - and focus on that. Treat them like a masterclass and think hard about what you want to talk about before going into it. It is easy to get distracted.
That is my take. I actually became friends with Baker and Nir as a result of these lessons. Oz invited me to hang when I come to NY. They were all great guys in addition to being some of the best players alive.
So yeah, I am a big fan of skype lessons w/ guys I admire.