You could write a routine that grab the vertices from one line, found the closest vertices in the other line, get the distance between those 2 vertices. Now you just need to sum all of the distances you grab from doing that operation above for each vertices, and divide by the number of vertices to get average distance between the lines. I would suggest doing this in python with the ESRI API's for python, but I believe it would also be possible in Model Builder.
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