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When the umpires called time, Zander de Bruyn was on 131 (18x4, 1x6), and Dale Deeb was on six.
McKenzie and De Bruyn started the partnership just before lunch, by which time the Lions had lost three wickets.
For almost two entire sessions, lasting some 65 overs collectively, they defied the Cobras bowling.
The Cobras eventually called on eight bowlers in an attempt to break the stubborn partnership.
At the start of play, the Lions were in a spot of bother after they were sent in to bat by Cobra's skipper Justin Kemp.
Opener Stephen Cook went without scoring, edging a Vernon Philander delivery to Andrew Puttick in the slips in the first over of the day.
Philander's new-ball partner Charl Langeveldt then trapped Jonathan Vandiar (14) leg before wicket and the Lions were reduced to 34 for two.
Prior to the lunch break, Philander struck again to remove Alviro Petersen (44), who seemed to be set for a big score.
McKenzie and De Bruyn scored at a steady pace, with both batsmen helping themselves to half centuries.
In the process they also guided the side's first innings total past the 200-run mark in the 54th over, and tea was taken in the 59th over when the total stood at 216 for three.
In the final session McKenzie went on to record his 38th first-class century, and De Bruyn his 23rd.
Even the new ball late in the final session failed to disturb the batsmen, but the introduction of Claude Henderson achieved the breakthrough as he captured McKenzie's wicket.
McKenzie's 145 included 19 fours and a six. Their 258-run stand for the fourth wicket bettered the previous best Lions' fourth-wicket partnership of 217, set by McKenzie and Vaughn van Jaarsveld earlier in the season.
Philander was the most successful in what was a long and hard day for the Cobras' bowlers with 66 for two off 19 overs.