When were you planning on lagering the beer? After the bottle conditioning?
What I would probably do is ferment at 50 degrees for 7-10 days or until the beer is ready for the diacetyl rest. After the diacetyl rest, I'd rack (and save the yeast) and begin lagering. Then when that batch was done lagering, I'd just start the second batch. It wouldn't really be "back to back" in the same way you propose, but it would be my preference because I'd like to harvest the yeast at the end of the diacetyl rest and and there isn't any need to leave the lager in primary for a month.
If you don't want to lager in a carboy, then you could speed up your schedule a ton by fermenting batch one until near FG. Then, bring the beer up for a diacetyl rest. After the diacetyl rest, bottle. Then make the second batch. After that one is raised for a diacetyl rest, bottle. Then lager all of the bottles after they are carbed up.
Lager yeast is easily rinsed and reused without a problem, so I'd go with the first plan I mentioned.