This is a reasonable approach, but there's a weak link in public key exchange. If Lavaboom (or any other trusted third-party) is facilitating public key exchange, there's nothing preventing them from saying "DE:AD:BE:EF" is Bob's public key when in fact it belongs to Eve the attacker. Not to say that Lavaboom would do this maliciously, but they might be compelled to do so by a state actor or law enforcement.

As a rule of thumb, a messaging system S can only be zero-knowledge if you have exchanged a secret or key with someone else outside of system S. See the HN discussion on iMessage: https://news.ycombinator.com/item?id=7315964