McKenzie, whose innings has now lasted nearly nine hours, was 131 not out at lunch with South Africa, following-on, 312 for one.
That still left them 34 runs short of making England bat again.
But they'd achieved their primary objective of getting through the session without losing a wicket, with McKenzie, on 128, surviving an lbw appeal from medium-pacer Paul Collingwood.
Hashim Amla was unbeaten on 57, having so far helped McKenzie add 108 for the second wicket.
There have been five consecutive draws at Lord's since Australia became the last side to win a Test here in 2005 and it was going to take something special from England to end that sequence in the first of this four-Test series.
South Africa resumed on 242 for one, having lost just one wicket on Sunday when captain Graeme Smith was out for 107.
They were still well adrift of England's first innings total of 593 for eight declared, which featured Ian Bell's Test-best 199 and South Africa-born Kevin Pietersen's 152 in his first Test innings against the Proteas.
McKenzie started Monday on 102 not out, with Amla 20 not out.
Initially in defensive mode on Sunday, McKenzie started to blossom and off Monday's sixth ball he cover-drove left-arm spinner Monty Panesar for four.
Amla again looked in fine touch and his ninth boundary, a cut four off a looping Ryan Sidebottom delivery, saw him to a 116-ball fifty.
Both batsmen were peppered by a succession of short-pitched balls, with England captain Michael Vaughan deploying a leg-slip and leg-gully, but all to no avail.
England's inability to take more wickets on a slow, batting-friendly pitch suggested they'd erred in selecting four main bowlers, including three seamers none of whom is an out-and-out quick, rather than opting for a genuinely five-man attack.
And with every wicketless over, the case for the recall of fast-bowling all-rounder Andrew Flintoff, who hasn't played Test cricket in over a year because of injury, for the second match of this series starting at Headingley on Friday grew stronger.
England's cause at Lord's wasn't helped by Sidebottom bowling while hampered by a back strain.
England Ist innings 593/8 decl Vs South Africa 247 and 312/1 (McKenzie 131 n o, Amla 57 n o, Smith 102; Anderson 1/66).