What a coincidence!
I went to my 3-and-a-pro clinic today, and the guy decides to teach this exact situation (with no prompting whatever by me). Here's what he taught:
Say Topaz and I are playing Raiden and Javier. I serve to Raiden in the deuce court and move in to net (split-stepping behind the service line). Raiden hits his first shot to my feet, and I hit an approach volley. Meanwhile, Javier and Topaz are in their net positions, shifting as appropriate with the ball.
Raiden then lobs his next shot over Topaz. Topaz has responsibility for that ball and is supposed to immediately decide whether she will play it. If she will hit her overhead offensively, she will say "Mine." I will then go to the deuce service line and wait there in case the overhead is returned.
If Topaz cannot reach the lob, she will say "Switch" or "You" or "Help. Topaz will then hurry from the ad court to the deuce court, at the side T, facing inward. From this position, she can see all three players and the ball. This is an intermediate position -- Topaz will decide where to go based on what she sees.
If she sees me struggling to reach the ball and Javier and Raiden salivating at net, she will scoot to the baseline. If sees me playing a groundstroke to Raiden at his baseline, Topaz will close the net and try to poach once my ball gets past Javier. If she sees my lob go over Javier's head and an ensuing scramble, she knows to position to hit a smash.
Topaz's intermediate position when I am hitting or chasing the lob is also helpful to me. I may be able to play the lob out of the air as a BH volley. If Topaz is completely out of my way, I have more options for placement. If Topaz is crowding the net in the deuce court or -- God forbid -- still standing at net in the ad court, she is restricting what I can do.
It took two hours for us to get the hang of this. It was actually pretty funny, as each of us had a different type of brain cramp. One lady simply could net get the words out when a lob went up. The other lady would say "Switch" and start running away from the ball even if the lob was going to drop right in the place she was standing. And I kept going after lobs that were way too deep, shouting "Mine" and then being unable to play the ball.
Now, my original idea was that I want my partners to fall off the net to the baseline when I am running down a lob that went over their head. Pro said there should be no need to do that when one's partner understands that she needs to call a switch and then take an intermediate position to assess the situation, falling back to the baseline if the situation is dire. Since none of my partners were doing that -- usually just moving sideways while remaining at net even if an overhead was coming -- I was calling them off.
The other thing that was interesting was that if you are already on your way to net, it is very easy to take lobs out of the air as high volleys. If you could get there before it bounced, it was a much easier shot than if you let it bounce. I never would have guessed that.
Man, doubles can be complicated. But fun!