England were 39 for one at tea after rain had washed out the entire morning session before bad light then stopped the match in only the 13th over.
Cook, dropped on one, was 10 not out and Jonathan Trott eight not out with England 2-1 up in this series after Pakistan's four-wicket win across London at The Oval last week.
It was no surprise when Pakistan captain Salman Butt opted to field first in fter winning the toss in the kind of overcast conditions that have troubled batsmen on both sides all series.
Poor catching has hampered Pakistan throughout this series and their 18th dropped effort in four Tests - a remarkable and damning statistic by international standards - was one of their worst.
England were on seven in the third over, when Cook was drawn into a defensive edge outside off-stump by left-arm quick Mohammad Aamer only for third slip Umar Akmal to drop the seemingly straightforward two-handed chance, much to the teenage bowler's evident and understandable disgust.
Next ball Cook added to Aamer's frustrations by edging him unconvincingly through the slip cordon for four.
Pakistan thought they had Cook caught behind off Aamer for nine, with England on 25.
Billy Bowden eventually gave Cook only for the Essex batsman, fresh from a century at The Oval to refer the decision.
Bowden, after replays indicated Cook had missed the ball, reversed his original verdict.
But Pakistan had the wicket their new-ball pair deserved when Mohammad Asif produced a superb full-length delivery that swung in a touch to bowl left-hander Strauss for 13 and leave England 31 for one in the 12th over.
Strauss has now gone over a year without a Test century and he may only have one more chance to end that run, should England bat again at Lord's, before England begin their defence of the Ashes in Australia starting in November.
Although the Lord's floodlights were on, Bowden and fellow New Zealand umpire Tont Hill halted the match midway through the 13th over after it appeared players were having difficulty seeing the red ball out of the otherwise dark background
Scoreboard
England 1st Innings
A Strauss b Asif 13
A Cook not out 10
J Trott not out 8
Extras: (W-5, NB-3) 8
Total: (for 1 wkts in 12.3 overs) 39
Fall of wickets: 1-31.
Bowling: Aamer 5.3-2-18-0; Asif 6-1-17-1; Riaz 1-0-4-0
