The New York Times announced Tuesday that Dan Lewis, the paper’s Week in Review editor, will replace Paul Goldberger as cultural news editor at the end of January.While Lewis has no specific experience in covering cultural news, he has been a highly regarded editor at the Times since 1977 and has run the Week in Review for the last 3 1/2 years. Goldberger, who won a Pulitzer Prize for his architecture criticism before taking the editor post in October 1990, will return to writing, with the title of chief cultural correspondent. Under Goldberger, the Times strengthened its Hollywood coverage, assigning veteran Washington reporter Bernard Weinraub to cover the film industry. Goldberger will split his time between writing for the daily paper and the Sunday magazine. Several editors outside and within the Times reportedly turned down the culture editor post — including Arts & Leisure editor Constance Rosenblum — leading to speculation that top candidates were uncertain they would have the authority to make substantial changes in the department. At a meeting Monday with executive editor Max Frankel and managing editor Joseph Lelyveld, Lewis asked if they had a “grand design” for the department. “They said no, and I found that curiously liberating” because it made him feel that he will “be more than a traffic manager and PR consultant,” Lewis said Tuesday.