You are doubtlessly right, though still fun to think about.
The law is (thankfully) not like code, and you can't always make a clever hack around the letter of it. When lawyers can, well, that' why they get paid well.
Then the lawyer couldn't delete the systems like Lavabit did because the government would have confiscated them as evidence of the conspiracy.
At that point, however, the 5th Amendment should apply, because the server provides evidence of a conspiracy the lawyer took part in, providing the encryption keys would also be providing evidence of the conspiracy; requiring the lawyer to testify against himself.
Some judges have tortured the 5th Amendment worse than this, so it's not entirely foolproof. Still, it's unlikely other lawyers would take this sort of abuse standing down, nor would the general public.
So even the most extreme legal logic I can think of would be unable to penetrate this arrangement, providing the computer security and encryption was all top-notch. Disclaimer: IANAL, though I'd be willing to be the IT employee for any legal firm that wanted to construct such a system.
Or even constructed such that the lawyer was central to all communication.
So client A contacts the lawyer to advise client B of X. The lawyer dutifully complies (perhaps in an automated fashion).
Whenever Client A wishes to contact another party who is not a client of the lawyer, the lawyer is given a client lead from Client A. The lawyer emails (the only time when mail goes to 3rd parties) the party, inviting him to go on his retainer so he can advise him on Client A.
While such a system would have to be automated, the system could delete any evidence of this automation, or at least plausibly deny specific instances of the automation.
Thus, all involved could argue the lawyer was manually involved every step of the way in the process, which only ever occurred on the lawyer's system, and the client systems of his clients.