The idea is LJ teams up with an outside company that provides voicemail boxes. LJ users can sign up for them for free (or perhaps all paid members get them) and then a small fee is collected every time someone sends someone a voicemail or when people check their voicemail more than x times per day.
We (as in the company I work for) just launched a similar product and it has a.) low startup costs and b.) huge potential. Best of all, it's c.) easy to add to the site. Since the third party is doing most of the work, all we have to do is add a link to the userinfo page to send them voicemail, add in a way to sign up for it, etc.
(Please note I'm not saying that it's no work, but it's less work than a lot of the new feature ideas since the other company does most of the work and absorbs most of the costs.)
Anyways I think it's worth thinking about. LJ has a lot of users and relatively low costs, currently, and this could potentially bring in a lot of money. If we tie it into paid user accounts it could even bring in more paid users.
P.S. - Incidentally, yes, I know there are issues with it, and I know a lot of users might not be able to use it due to being teenagers sans ways of paying, but the same is true of paid member accounts. Since the cost to LJ would be almost nothing it wouldn't be a huge risk financially, and if even 10 people used it regularly it'd pay for itself. If, say, 1000 people did, it could bring in more money than the paid account subs. themselves.
P.P.S. - there's a 900 number for leaving voicemails. So anyone who can call 900 numbers without getting busted by their parents can use the service. Again, with 300k members I'm sure there are enough that fit that profile that it could work.