Not so sure about this bit.
First, you can't plan in advance who should take the lob because you don't know what kind of lob it will be.
Second, if the net player is going to overhead the ball (hopefully by saying "Mine"), the server is supposed to come to the service line, ready to deal with any reply to the overhead, right? If the server hovers to back up the net player, the server may be out of position to deal with a ball that squirts off of the opponents' racket off of the overhead.
I didnt say they need to go to any special position to backup their partner, I just said they have to be ready. (it can be on the service line, I certainly didnt mean they run behind their partner and wait ahead of time)
If they are not ready, you can yell "SWITCH" all you want and it's not going to matter. If they are ready they have eyes, they can see what's going on, not to mention that there are tons of lobs that clearly are not going to get intercepted by their partner so they should be shagging them down as soon as possible. (which is the part that they should be aware of ahead of time)
I think we get caught up into this sort of thing though because many of us has 20 different partners in a short period of time ,and many times maybe we get stuck with a new partner in a real match for the first time.
If I play with someone a lot, we dont have to say as much, everything just flows a lot nicer. We save all the excess communication for the unique situations that dont come up quite as often, not frequent ones that we both sort of already know our role on.
I think the answer to your OP question really depends on your partner though and your faith that they are going to somehow shag that lob down and do something productive (or at least get you out of trouble with it).
If they are awesome at clearing net players!!!!! Then I'd stay at the net. Although that also depends on if my opponents are smart enough to realize they should close in or not themselves. (if one of them stays back I can feel safer at the net)
If you are not so sure, then you need to backup to the service line at least. Or if your opponents are both now ready to close into the net (especially if they are on the service line and not closer because you know they can close in if they need to and they can pick off a lob attempt easier)
If you think you are in real trouble though then get back to the baseline. If you can make it there in time and still be ready for the next shot...... If you smell an obvious overhead pending, that's where you are going to wish you were anyway.....
So it all depends on the 3 other people on the court, not just some blind idea of "what should I do???" according to some book or some question on the TW forum.