That's a tough one! I'd like to hear other people's insights as well - not so much so that I can play like that, more in order to get a deeper appreciation of the Phil Zone.
I did find an article online: The Musical Imagination of Phil Lesh: The Grateful Dead's Difference Engine
by Brent Wood - haven't had a chance to dive in but this caught my attention because it's what I have found through my own listening:
"Lesh’s playing, in a general sense, relies on long, non-repeating phrases composed of series of brief melodic figures which swing around the main harmonic downbeats, forming obtuse counter melodies to the implied central melody."
I saw him perform a few months ago with his group at Terrapin Crossroads, and they played "Proud Mary" - on the second time around he didn't reinforce the riff that opens the song, he was noodling around up high instead. It sounded thin and I was really surprised, then I remembered who I was listening to! So often he doesn't play what you would expect a "normal" bassist to play, and at times I find it disconcerting. But then when he does something like reinforce the riff or pump root quarter notes, it's that much more powerful.
There was an issue of Bass Player where they offered an analysis of Phil's style and a transcription of "Scarlet Begonias" (I think) - not available online anymore but I'll see if I can find my copy (if I still have it) and scan it. I did find this quote that I had copied though:
“I went in with the idea I didn’t want to be a standard bassist,” he says. “At that time, who played anything interesting in rock & roll bass? There wasn’t anything going on, and I didn’t want to be relegated to the role of just thumping along. I wanted to bring a more fluid, melodic approach to the instrument.” With little background in pop music, Lesh drew instead on his classical training—particularly contrapuntal composers such as Bach and Palestrina—for inspiration. “In counterpoint the bass line is a melody, as are all the other lines, yet they all fit together. They move at different speeds sometimes, but it’s always interesting, and it’s always linear. The voices always lead somewhere.”