On June 8, Daddy’s Diner got a taste of the limelight. The Richmond-based eatery was rented out and became a TV set, as Farm Journal, Pivot Bio and Fivestone Studios shot the project “Farmers’ Table.” The web series/TV program invites farmers from around the country to converse about niche topics. Farm Journal will share “Farmers’ Table” on its website, www.farmjournal. com. And several months after editing, it will air on RFD-TV. Rockie Britzmann, a manager with Fivestone, said the Daddy’s episode would be the second one in the series. Tyne Morgan, a former Lexington resident who works as a TV host on the “U.S. Farm Report” with Farm Journal, suggested Daddy’s. When she heard that project sponsor Pivot Bio was seeking a place to film, the diner “immediately came to mind,” Morgan said. Brian Conrady, who works with Morgan, acknowledged Morgan’s recom mendation was key. “When we go out, we want authentic diners that farmers go to,” Conrady said. “And this is it. … She came here…