With their doors blocked by gas lines, their customers stranded by cab strikes and their dining rooms turned into deserts by President Carter's thermostat rules, Washington's restaurants are in trouble.

Short lines at lunch and empty tables at dinner are the symptoms of an energy-inspired exodus from the District of Columbia's 1,000 restaurants, the biggest retail business in the city.

The last two months have been slow all over the metropolitan area restaurateurs report, but especially so in downtown establishments and especially on weekends.

Business is down as much as 30 percent, restaurant owners say. Food prices are up by a like amount, creating a cash-flow crisis that could close the doors of some struggling cafes.

"Some people just will not be able to make it, especially places that are not quite known yet," warned Jean Michel Farret, maitre d" at Jean-Pierre, the French restaurant on K Street NW.

I look to see a lot of people running to the bank and squeezing their suppliers," agreed Barbara Witt, proprietor of the The Big Cheese in Georgetown.

Farret said business some days is off 30 percent from a year ago and Witt said her June and July volume to date is precisely 7.5 percent less than during last year.

When two of the most successful eateries in the district of Columbia report that kind of a slump, it indicates serious difficulties for the city's biggest retail business.

"It's a two-pronged problem," explained Lee Palmer, owner of the Old Club in Alexandria and president of the Restaurant Association of Metropolitan Washington.

"Tourist business has declined directly due to the gasoline situation, and when it declines, all the economy declines with it," he added.

Palmer said that during the first week of the gasoline crisis, some restaurants reported a 50 percent drop in business but things have picked up since the gas lines began to shrink.

Like many suburban restauranteurs, Palmer said his business has not been hurt so badly. "My customers stayed home and came to eat with me," he explained.

Fast food and family restaurants - the places that emphasize convenience and cost rather than cuisine - apparently are faring better than more elite eateries.