Norrie, 27, took a 2-1 lead after three sets against the 21-year-old but let his advantage slip to leave Andy Murray and Dan Evans as the only remaining British players in the major tournament across the men’s and women’s singles draws.
Norrie also received treatment on his left knee early on in the deciding set.
“I can’t really put my finger on why I wasn’t at my best, he played better than me and better in the bigger moments,” Norrie said.
“The knee did not affect the outcome of the match — it was a small niggle and I wanted to check it was nothing serious.
Lehecka had the measure of Norrie, the No. 11 seed for the tournament, and said their warmup match in Auckland on Jan. 11 helped him learn about his opponent’s resilience.
“I felt that I could beat him,” Lehecka said after the match. “It was a great match. Cameron was playing incredibly.
“The only thing I learnt from that match [against Norrie in Auckland] was to never give up and fight for every ball.
“I feel amazing and ready for the next round. Last year playing four Grand Slams for the first time and never going past the first round.
“I knew I could beat this guy. I’m super happy that I’m through and of course it is not the end.”
Lehecka will face No. 6 seed Felix Auger-Aliassime in the fourth round.