LastPass does it the usual way - they've got a premium (enterprise) product which they sell for $12-$24 per user per month. They can then write off any losses from the free product.
That's $12-$24 per year, not month. And they can do it simply because of sheer volume. Everyone has to deal with passwords so their market is humongous. If you sell to teachers that's not the case.
Selling to 100 users inside of one company is a lot different than selling to 100 individual users scattered all over the place. Company IT is likely to be the first point-of-contact for issues, which would decrease LastPass's support requirements by quite a bit.