Not sure we're "big league", but we do what you say: a big ol' export from LightSpeed then imported into
MailChimp.
One bummer is that LightSpeed doesn't have a way to bulk remove email addresses. So when people unsubscribe, bounce, or mark as spam, you have to remove people one-by-one. Fortunately, at least MailChimp (probably same for Constant Contact, Campaign Monitor, etc.) will never send again to an address that unsubscribed, so even if you miss a few you won't accidentally spam anyone.