The grieving process for The New Group's production of ''Mourning Becomes Electra'' will be a brief one. The revival of the Eugene O'Neill drama at the Acorn Theater has moved up the closing date for its limited run by six weeks, a publicist for the show said. The play will now close on Sunday; it was originally scheduled to run through April 18. No reason for the early closing was given, but the play, a 4-hour-10-minute restaging of the ''Oresteia'' in 19th-century New England, received mostly poor reviews, despite a cast that included Lili Taylor, above with Joseph Cross, and Jena Malone. [ABSTRACT FROM PUBLISHER]
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