He remains important to Arsenal manager Unai Emery, however, and was handed the armband against Newcastle in the absence of regular captain Laurent Koscielny, who was out injured.
He thought he had put Arsenal ahead in the 13th minute when he side-footed home a far-post finish after a corner was flicked on at the near post.
But the goal was disallowed because Sokratis Papastathopoulos was tugging the shirt of an opponent.
Ramsey got his goal soon after, though.
He flicked a pass to Lacazette, who was dispossessed just inside the area. The ball ran loose and Ramsey pounced to send a first-time shot through the legs of Paul Dummett and in off the post from 15 metres.
His night ended prematurely when he suffered an injury in the 66th minute and immediately signalled to come off.
At that stage, Newcastle were still in the game despite never seriously threatening Arsenal goalkeeper Bernd Leno.
Lacazette secured the win when he ran onto a header by substitute Pierre-Emerick Aubameyang and lobbed the ball over goalkeeper Martin Dubravka.
Arsenal rose back into the Champions League qualification spots and have possibly the most benign set of fixtures of the four teams chasing a top-four place behind title challengers Liverpool and Manchester City.
Arsenal are two points clear of north London neighbours Spurs and Manchester United with seven matches still to play, with Chelsea a point further back.