New Zealand 378 and 62 for 2 (Latham 30*, Robinson 2-8) lead England 275 (Burns 132, Southee 6-43) by 165 runs
Having come into this Test as the No. 2-ranked side, and preparing to contest the inaugural World Test Championship final later this month, it perhaps should not come as a surprise to learn that New Zealand have controlled this game. Were it not for the fact that the entire third day was lost to rain, they would be well on their way to winning at Lord's for only the second time 18 attempts.
Tim Southee bowled with skill and guile to claim a six-wicket haul - the second time he had done so at this ground - and it took a doughty century from Rory Burns to keep England clinging on by their fingertips.
The visitors still claimed a 103-run lead on first innings, but Burns' defiance and a pair of fighting stands with the lower order had kept them in the field until tea. Had Burns been stumped off Mitchell Santner on 77, England would have been 193 for 7 and New Zealand might have had a genuine window of opportunity.
As it was, New Zealand adopted a circumspect approach to their second innings. Devon Conway took his match tally to 223 runs - the most by an opener on Test debut - before being bowled off an inside edge by Ollie Robinson, who also removed Kane Williamson lbw for 1. With 62 runs being scored from 30 overs, the chances of either side being able to set up the game on day five receded.
Robinson's interventions followed a vital 42 with the bat, and kept him right in Conway's slipstream for most-impressive debutant. He became the first bowler in the match to find a way through Conway, and then twice pinned Williamson in front of his stumps with consecutive balls - the first lbw appeal was given, only for technology to detect an inside edge; the second wasn't, but England finally found success with a review, having already burned two of their three.
England's efforts to stay in the game were worthy of praise, although they have been outplayed on two days out of three. Burns produced a typically gritty knock for his third Test century, and first since November 2019, but a callow batting line-up struggled to deal with the threat of Southee and Kyle Jamieson, with three ducks and a 2 registered among the top seven.
After Friday's washout, and with England still only two down in their first innings, this game needed a powder keg placing under it. Jamieson gave New Zealand the perfect start, removing Joe Root with the first ball of the day - England's captain walking back with the clock still showing 10.59am - and Southee did his best to reduce the England innings to rubble with three wickets in as many overs. But Burns and Robinson dug in for a 63-run stand to narrow the deficit and take time out of the day.
Southee completed his second Lord's five-for by removing Robinson with the second new ball and England's position was still a parlous one, as Mark Wood and Stuart Broad fell cheaply. Burns, who was also dropped at slip off Neil Wagner on 88, was still nine runs short of his hundred when joined in the middle by James Anderson, but he pilfered seven runs in the next over - and Anderson survived two dot balls from Jamieson - before steering Wagner to third man to reach the landmark.
Burns scored just 13 runs during the morning session, putting a price on his wicket as his team-mates came and went, and had added 32 from 127 balls up to the point that the ninth wicket fell. But Burns cut loose during a 52-run stand with Anderson, taking Jamieson for three fours in an over and launching Wagner into the Mound Stand for his first six in Test cricket. He was eventually last man out, feathering Southee through to BJ Watling.
That passage further delayed New Zealand's progress, after hopes of being able to push for victory had been raised by a rip-roaring morning during which they claimed four England wickets in little more than an hour. Any thoughts Root had of attempting to guide his team towards parity were banished by Jamieson's opening delivery, which pranced and straightened from a length, clipping the outside edge to be scooped low by Ross Taylor at first slip.
Ollie Pope, a relative veteran of 18 Tests, twice edged Jamieson for fours wide of the cordon but stroked three more genuine boundaries in his 22, only to be pinned in front of his stumps by Southee - although it needed the help of DRS after Michael Gough turned down the initial appeal. Dan Lawrence, playing his first Test at home, then edged his second ball to slip and the debutant James Bracey was castled for a duck as England lost 3 for 0 in 21 balls.
Robinson needed a review to survive until lunch after being given out by Gough caught at short leg in Mitchell Santner's exploratory over, as England went in six down and still short of the follow-on target. Santner then should have removed Burns after the interval, only for Watling to fail to collect the ball. In the end the partnership was broken by Southee, as Robinson picked out long leg trying to take on a bouncer - but not before he had held up New Zealand for almost two hours.

Alan Gardner is a deputy editor at ESPNcricinfo. @alanroderick