J.J. Abrams apparently does not want to be contacted.
He’s not on Twitter. There was an account for a JJ_Abrams, but it was a hoax and was taken down.
The website for his production company, Bad Robot, has a page with the company logo and nothing else.
Clicking on the URL of a fan site, the J.J. Abrams Universe, gives an error message, at least when I checked.
It seems, in the immortal words of Greta Garbo, that he vants to be left alone. Or perhaps he just vants to avoid receiving truckloads of random screenplays.
On the other hand, Damon Lindelof and Carlton Cuse, the joined-at-the-hip, writing-slash-executive-producing, often-joking, panel-discussion-appearing, interview-granting, commentary-track-recording dynamic duo, provide the public face of the LOST team and are easy to find. Both are active and interesting Twitter users. You can follow them at @DamonLindelof and @CarltonCuse.
By the way, according to Lostpedia, “Abrams will not be involved with Season 6, as he thinks that Damon and Carlton themselves should finish what they have been doing with the show. He also rejected the idea of directing the series finale, since he thinks Jack Bender has earned himself that right.”