India have their own injury concern after wicketkeeper Rishabh Pant spent most of the day off the field following a blow to his left index finger.
Like Stokes, Pant had one round of treatment on the field before being hit for a second time attempting a take down the leg side off pace bowler Jasprit Bumrah.
He was not seen after the 34th over of the day, with substitute Dhruv Jurel stepping in behind the stumps and holding an excellent catch to dismiss Pope.
The tourists have no plans for Pant to have an X-ray before the second day begins.
Pope, who was dropped off his first ball, made 44 in a third-wicket stand of 109 with Root.
On a slow pitch at Lord’s, against some excellent Indian bowling, England were forced to curb their attacking instincts. A run-rate of 3.02 per over is their slowest for a total in excess of 200 since Stokes became captain three years ago.
“It’s not necessarily the way we’re used to going about a first innings, but I think 251-4 is a pretty good score at the minute,” said Pope.
“Obviously we would have liked some more runs, but the nature of the surface and the way the Indian attack bowled was pretty good.
“It’s a day we’ll take. We had to adapt the way we play, but hopefully it’s a score we can really kick on from tomorrow and make it north of 400, towards 500.”