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NOPE! but good eye:

The expression, "the smoking lamp is lighted," is older than the United States of America. It is the word that is "passed" when it is all right to light up a cigarette, pipe or stogie. When it's time to stop smoking (e.g. during the loading of ammunition), the word is "the smoking lamp is out.

Scrub and Wash Clothes or Pipe Down Your Scrubbed and Washed ClothesOrder to wash clothes after the decks are wet down.Scrub Bags (Hammocks or Mattress Covers) (as the case may be)Order given on certain days after the washing of clothes.Scrub Down the Decks With (Without) Sand; Scrub the Paint WorkPerform this work as directed.Secure From Darkened Ship or Light ShipResume conditions of lighted ship. The smoking lamp is lighted unless otherwise ordered.Secure From Battle Stations General Quarters (Set Condition Two/Three, Watch 1, or 2, or 3)Certain battle stations are made fast or secured, and others left manned according to the condition of readiness ordered.Shift to Uniform of the DayAll hands shift into uniform of the day except as directed to do otherwise.Slack Off HalyardsTo give slack to the hoisting lines in wet weather to prevent lines from becoming too taut.Smoking Lamp Is LightedSmoking is permitted throughout the ship, or in a designated area of the ship.Smoking Lamp Is Out (or Out On the Foc'sle)No smoking is permitted in the ship or in a given area of the ship.Spread AwningsStretch awnings in place.Stand By Your HammocksGo to hammock nettings or bunks and face aft.

http://www.history.navy.mil/browse-by-topic/heritage/terminology/manual-of-commands-and-orders-1945.html I would imagine, given the archaic speech form, that it stems from the day of clay pipes and cigars not to confused with the "gunners matches are lighted" when called to general quarters in the days prior to flintlock ignition battery's. WE wouldn't want a 'powder monkey', generally a lad, to explode servicing the guns in battle much less the loose powder-bag spilled in the heat of conflict.

Sea dogs who sailed the wooden ships endured hardships that sailors today never suffer. Cramped quarters, poor unpalatable food, bad lighting and boredom were hard facts of sea life. But perhaps a more frustrating problem was getting fire to kindle a cigar or pipe tobacco after a hard day's work. Matches were scarce and unreliable, yet smoking contributed positively to the morale of the crew, so oil lamps were hung in the focsle and used as matches. Smoking was restricted to certain times of the day by the bosuns. When it was allowed, the smoking lamps were lighted and the men relaxed with their tobacco. Fire was and still is the great enemy of ships at sea. The smoking lamp was centrally located for the convenience of all and was the only authorized light aboard. It was a practical way of keeping open flames away from the magazines and other storage areas. In today's Navy the smoking lamps have disappeared but the words smoking lamp is lighted in all authorized spaces remains, a carryover from our past.

<enlarges; note that nervous powder monkey on the left...I recollect Black Beard notoriously wore his matches to instill terror><it's good to B captain...the 'lamp is always lighted' < case in point: 118 gun L'Orient blows up at the Battle of the Nile: a morale lessening turning point of the battle. 70 men of her crew of 1130 were rescued. Shortly after the battle, Nelson was presented with a coffin carved from a piece of the main mast of Orient, which had been taken back to England for this purpose; he was put inside this coffin after his death at the Battle of Trafalgar. Modern archaeology suggests two simultaneous explosions did in the great flagship. Somethin' sure was lit !