The Segunda Division side reached the round of 16 with victories over Mallorca, Eibar and Granada in 2013-14, but fell at the first hurdle this time.
Lolo's 77th-minute goal was enough to secure a memorable victory for Lugo and give them a place in the third round for only the sixth time in their history.
The tie looked to heading for extra time before the flow of the game changed midway through the second half when Alcorcon defender Chema received two yellow cards in quick succession.
The 22-year-old received his first booking just after the hour and six minutes later he was shown second, and a subsequent red, to leave his team a man short for the last 20 minutes.
Lugo took full advantage and, with 13 minutes remaining, Lolo struck the decisive blow to put them in the hat for the draw for the next round later this month.
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