Singh missed a 6-foot par putt at No. 18 that would have given him the outright lead at the London Club. He and Lorenzo-Vera were at 8-under 136, one stroke ahead of Anthony Wall of England (69) and Christian Cevaer of France (70).
First-round leader Anders Hansen was two behind after a 73. He is one in front of Peter Hanson, who also had a 73.
A number of big names missed the cut at 1 over, including John Daly (76), who later said he would not play the Wales Open next week.
Others to miss the cut were Masters winner Angel Cabrera (75), defending champion Ross Fisher (73), fifth-ranked Henrik Stenson (80) and Shane Lowry (73), the Irish Open winner two weeks ago who was playing his first pro event.
The 18th has a narrow fairway with water on the left and thick rough on the right. In a stiff crosswind, it didnt yield a birdie all day.
In this wind, there is not any tougher tee shot than that in the whole world, said Graeme McDowell (73).
Before Singh bogeyed the last, he chipped in on the preceding hole.
The lie wasnt too bad but out of the rough you dont know how the ball is going to come out, he said. Honestly, it just came out too hot for me and would have gone at least 10 feet past the hole. Luckily, there was a flag there.
Lowry was resigned to missing the cut after his opening 76, but will play the Wales Open at Celtic Manor, where next years Ryder Cup will be held.
For the last 24 or 25 holes of the 36 I played good golf. But my putting let me down, he said.
Cabrera missed the cut for the third time in four events since he won at Augusta in April.
Lee Westwood (75) and European Ryder Cup captain Colin Montgomerie (74) both survived.
I played very poorly. It was disappointing, Montgomerie said.