LCT3 now has a home.The fledgling Lincoln Center Theater division dedicated to producing work by emerging playwrights, directors and designers will stage its productions in the Claire Tow Theater, a new dedicated space being built on the roof of LCT’s Broadway house, the Vivian Beaumont. Construction will begin in spring on the 23,000-square-foot, two-story addition, designed by architect Hugh Hardy of H3 Hardy Collaboration Architecture. Budget is $41 million. New structure will also include office and rehearsal space, with completion anticipated in late 2011-early 2012. Theater is named after the wife of longtime LCT board member Leonard Tow in recognition of the Tow Foundation’s support. LCT has raised 90% of construction costs prior to the public phase of its capital campaign. Addition of the Claire Tow brings LCT’s permanent houses to three, with the Beaumont (home to the hit “South Pacific” revival) and Off Broadway space the Mitzi E. Newhouse Theater, where David Cromer’s production of Andrew Bovell’s “When the Rain Stops Falling” bows Feb. 11.Since launching in fall 2008, LCT3 productions including “Clay,” “Stunning” and “What Once We Felt” have been staged at a rental house, the Duke on 42nd Street. Next up in the series at that venue is Ellen Fairey’s Chicago hit “Graceland,” directed by Henry Wishcamper (May 3-29), followed by Lear DeBessonet’s production of “On the Levee” by Marcus Gardley, with music and lyrics by Todd Almond (June 14-July 10). Paige Evans is director of LCT3. New venue reps further evidence of the commitment by New York’s nonprofit theater companies to nurturing new talent. Roundabout, Manhattan Theater Company and Atlantic Theater Company are among those that also program stages dedicated to emerging voices.