The British number one struggled initially in breezy conditions but looked to be on the right path when he opened up a two sets to one lead.
But 21-year-old Lehecka, ranked 71 in the world, battled back to take the second and Norrie took a medical timeout for treatment to his left knee early in the fifth set before falling to a 6-7(8), 6-3, 3-6, 6-1, 6-4 defeat.
It will be a big disappointment for Norrie, who beat Lehecka on his way to the final of the ATP tournament in his home town of Auckland last week and had started the season by defeating Rafael Nadal and Taylor Fritz at the United Cup.
In hindsight, Norrie may feel he played a little too much in the build-up, and he was not able to find the same form here that he showed in Sydney.
Czech tennis has largely been about a remarkable production line of female talent but Lehecka is one of a cohort of young men hoping to emulate the success of Tomas Berdych.
He possesses a big serve and forehand and had the better of the first set, forcing Norrie to save three break points, but could not convert a 6-4 lead in the tie-break.
Norrie showed his competitive desire to save three set points, the first with a fine pass down the line, and clinched his second opportunity.
But the 27-year-old was not playing well, missing time and again with his forehand, and Lehecka held onto an early break to claim the second set.
Norrie appeared to have found his range in the third, making only six unforced errors compared to 27 in the first two sets, but the momentum switched around again at the start of the fourth.
The 11th seed was in big trouble when he dropped serve again in the first game of the decider and called the trainer to have his left knee taped up.
Norrie fought hard to try to find a way back after going a double break down but he was unable to conjure the same magic as Andy Murray and Lehecka served the match out to love for the biggest moment of his young career.