The German fifth seed, who fought his way through a five-set thriller in the opening round, threw away a two-set lead against the 30th seed on Court Simonne Mathieu before setting up a meeting with Fabio Fognini.
It was a highly inconsistent performance by the lanky 22-year-old Zverev, who will need to sharpen his focus against the Italian ninth seed. Fognini progressed with a 7-6(5) 6-4 4-6 6-1 victory against Spanish 18th seed Roberto Bautista Agut.
Zverev did not make things easy for himself as he fell 3-1 behind in the opening set before managing to turn things around and take the lead.
He raced through the second only to find himself on the back foot again in the third and fourth as Lajovic forced a decider with temperatures flirting with 30 degrees Celsius — a contrast with the chilly weather in the first week of the tournament.
After an early trade of breaks in the fifth, Zverev finally got his confidence back and finished it off with a whipping forehand, his 52nd winner barely making up for a woeful 55 unforced errors.
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