You really do not understand what is going on here.
Hushmail would have the exact same problem, Hushmail is not all that different from Lavabit.
When you load a message from your hushmail encrypted inbox it is DECRYPTED on the server side using the password you provided at login, then the HTML representing the email contained in your inbox it is then ENCRYPTED by the web server using SSL and Signed Certificate that is recognized by a web browser, in Hushmails case that CA is thawte, in LB case the CA was GoDaddy and sent to you.
ALL HUSHMAIL USERS share the same SSL Encryption from the Hushmail server to their Browser, this is how the web works. There is no changing at least not by a single company.
The only way around that would be to not use HTTP, or web browsers. But then you could create an entire new messaging system like BitMessage, but LavaBit was attempting to give people private EMAIL, not create a new messaging protocol