From FAA "lessons learned" report on AA 191 Accident:
The NTSB concluded that the airplane was being flown in accordance with American Airline's engine failure procedures. Immediately after liftoff, a pitch attitude of 14 degrees was attained and maintained, indicating use of the flight director for pitch guidance. It was also subsequently determined that the captain's flight director was inoperative, implying that the first officer was flying the takeoff. American Airlines procedures required that, following an engine failure, the airplane should be accelerated to V2, and climbed to 800 feet at that speed. No differences in the procedure were specified if an engine failure occurred after reaching V2, and in fact, the specific scenario was not addressed by the airline's procedures. Following the accident, American Airlines modified this procedure to either maintain the speed at the time of engine failure, if between V2 and V2 + 10, and to maintain not less than V2 + 10 if the failure occurred after reaching V2 + 10. The revised procedure also instructed crews to disregard the flight director pitch command (which provided guidance to achieve V2) and to maintain at least V2+10.
It was clear to the NTSB that the airplane was being decelerated from 172 knots toward V2 in an attempt to follow the engine-out climb procedure (and reacquire V2) when the left wing stalled at 159 knots. The stall resulted in the left roll and ensuing loss of control.