City fell agonisingly short of getting something from Tuesday night's trip to league leaders Rotherham United despite an impressive second-half performance at the AESSEAL New York Stadium.
Two goals inside four minutes gave the Millers an early lead, but they were left hanging on after the Imps turned around the balance of play in the second period.
Tom Hopper pulled a goal back but despite some great build-up play, the visitors could not find a way past former City goalkeeper Josh Vickers who pulled off important saves when needed by his side.
Attendance: 9,575 (1,209 away)
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