British duo Cameron Norrie and Jack Draper ramped up preparations for the Australian open with victories in the ASB Classic and Adelaide International 2 respectively.
Norrie missed three break points in the fifth game of the first set before a spate of unforced errors allowed Lehecka to break for a 4-2 lead, but the British number one quickly got the contest back on serve.
Norrie broke once more in the ninth game before holding to clinch the first set, but after squandering more break points in the second, Lehecka edged the tie-breaker to force a deciding third.
Four unforced errors from the Czech player allowed Norrie to storm into a 3-0 lead, and he held convincingly to wrap up the win in two hours and 45 minutes, but severe rain delays meant that the six-hour mark had passed before the match ended.
After winning 79% of points on his second serve and setting up a quarter-final with Marcos Giron, Norrie said on the court: "It's tough on the concentration.
"Credit to him [Lehecka], he really took it to me. I really enjoyed the time on centre court, it's good to be back in New Zealand."
Meanwhile, rising star Draper reached his first ATP quarter-final of the year after comfortably getting the better of the American Paul, doing so in one hour and 31 minutes in Adelaide.
Paul earned the opening break of the match and established a 4-1 lead in the first set, but Draper came storming back to win the next five games, firing back-to-back aces to move 1-0 up in the match.
After breaking in the third game of the second set, the 21-year-old beat away three break points in game eight to hold, but Paul would proceed to hit consecutive aces to force Draper to serve out the match.
Despite registering his only double fault of the day, Draper posted two more aces - taking his total up to 10 for the day - to march to an emphatic two-set victory, winning 88% of his first-serve points along the way.
The world number 40, who had already got the better of Italy's Lorenzo Sonego in the first round, now faces a challenging rematch against Russia's Karen Khachanov - who eliminated him from the Adelaide International 1 - for a place in the semi-finals.
Finally, Andy Murray - who lost in the first round of the Adelaide International 1 last week - overcame China's Zhang Zhizhen 2-6 6-3 10-2 at the Kooyong Classic exhibition event in Melbourne, recovering from going 5-0 down and ceding the first set to prevail.