I'd never heard of Lavabit before; it looks like they're still operational, although their website hasn't been updated much since around 2007. Looks interesting. I'd really like to see a high-quality secure email provider get wide adoption.
Can you break down what "high-quality" means for you? eg Web UI, specific features, hosted/self-hosted etc. Are you rolling your own at the moment or on gApps? I've started looking into this with a view of building something so understanding what's important to folks is v useful.
What I want: 0) User selectable/delegable domains (it's ok IMO to use yahoo/gmail/aol/etc. today, if you know and accept the limitations. It's moronic or at best short-sighted to depend on an @yahoo.com, @gmail.com or @aol.com address, though.) 1) IMAP/activesync (push; imap-idle is nice but not sufficient) 2) Good anti-spam 3) Sane and/or configurable account-recovery procedures. Since email is essentially the master-key to your other accounts which use email-from auth for password recovery, it's a big target. This is a hard technical and policy problem. I'd like it to be something users can configure at account creation time in various ways, ranging from SMS/call from to "can't recover password". A good medium might be "takes 3-7 days to recover password with notification given in advance to all other means of contact, must use postal mail to confirm" or something like that.
It would also be nice to have: 1) Great search 2) Ideally, a webmail client. Ideally, as nice a webmail client as possible 3) Encryption wherever possible. The low hanging fruit is start-tls for SMTP and IMAP, and https for the webmail. Storage encryption would be nice; could be "encrypt mail to a public key as it arrives". 4) Support of S/MIME (and PGP, ideally) keys would be really nice; do some signature checking on the server side in the webmail ui? Run a keyserver? Issue s/mime identities to people who use accounts on your domain? Partner with a CA? 5) Configurable retention policies 6) Group/team/business features (address books) 7) Maybe calendaring 8) Maybe voice/sms too