I don't think so. There's a big difference between the legal firepower available to a small service provider like Lavabit and someone like Yahoo or Google -- and handing over the ability to read everything is definitely not something that a simple warrant can legally require. Nor even an NSL.
There's also a difference in the willingness to fight of someone like Yahoo or Google, as already well demonstrated. Neither company would shut down rather than comply if faced with such an order.
Lavabit wouldn't shut down rather than comply with the original warrant, either. In fact, Lavabit eventually decided to comply, but given the nature of their system and the way they'd tried to obstruct the warrant initially, the feds didn't trust them to comply and do demanded total access, with the support of the court. Lavabit chose to shut down rather than throw the doors open.
Google and Yahoo would have complied with the initial, narrow request, so the sweeping demand would never have come up. But if it had, I really doubt they'd have rolled over. I'm certain Google would have refused, at least.