This is a question deserving a brief answer! I think you are on the right track wanting to have your lager fermentations timed where you can use the same lagering schedule. I strongly discourage you, however, to delay pitching the first batch for an entire day because that is a recipe for a potential bacterial disaster.
Most lagers have three phases to fermentation: primary fermentation, a diacetyl rest and lagering. Let’s assume that primary fermentation takes seven days for both batches at 50 °F (10 °C) and you add another four days at 68 °F (20 °C) for the diacetyl rest before chilling the beers to 32 °F (0 °C) for lagering. It will not hurt the first batch at all if you simply extend the diacetyl rest to five days so that both beers are chilled at the same time. This scheme will solve your timing problems and eliminate the big no-no of delaying yeast pitching. Happy lagering!