The 24-year-old was on the verge of his £75m move from Everton to Old Trafford when he was arrested in Los Angeles where he was holidaying with close friend and now team-mate Paul Pogba.
He had allegedly already received five verbal warnings from police over a five-day period.
The Belgian international, who is currently on international duty, did not appear in court himself in LA on Monday but his lawyer, Robert Humphreys, entered a plea of not guilty on his behalf.
Commissioner Jane Godfrey, who is overseeing the case, adjourned the case to Los Angeles Airport Courthouse on 21 November, although Lukaku is again expected to not appear in person and opt to send his lawyer on his behalf.
If found guilty, Lukaku faces both a fine and paying a sum to cover the cost of the police call-outs that occurred over the course of the five days.
Lukaku joined United eight days after his arrest on 2nd July and has so far scored 11 goals in 10 games.