Libby made 54 and Patel was undefeated on 51 at the close, when the second of two stoppages for bad light forced the players off with 4.2 overs remaining.
By that stage Notts had progressed to 303 for five, a lead of 27, with Riki Wessels also unbeaten, on 25. Kyle Jarvis and Jordan Clark had each taken two wickets for the visitors.
Earlier, Lancashire had lost their final wicket to the 11th ball of the day, to be bowled out for 276. Imran Tahir trapped Matt Parkinson lbw to finish with figures of four for 81.
Responding, Nottinghamshire’s openers quickly made inroads into the Lancashire score by putting on 86 together.
Steven Mullaney set the tempo by punching the first ball of the innings through midwicket for four. The bowler, Neil Wagner, had happily recovered after being struck on the helmet while batting on the first day.
Mullaney had a life on 33, being spilled by Parkinson in the deep off Jarvis, but fortune swung back in favour of the bowler as the former Lancashire player chopped onto his own stumps a couple of overs later.
Lancashire came out fighting at the start of the afternoon session and snared two wickets in quick succession. Libby was caught behind by wicketkeeper Steven Croft, from the bowling of Wagner, for his lunchtime score of 54. The 23-year-old right-hander had made his runs from 78 deliveries, with five fours.
Greg Smith then perished at the other end, trapped lbw by Jarvis for 30, but Michael Lumb and Brendan Taylor breathed new life into the home effort with a fourth-wicket stand of 74.
Taylor had been very watchful at the start of his innings and took 19 deliveries to get off the mark but he then blossomed into an array of attacking shots and twice galloped down the track to loft Parkinson’s leg-spin away for straight sixes.
But attempting an uppercut against Clark just before the tea interval, the former Zimbabwe captain picked out Tom Smith at third man for 37.
A sharply taken catch off his own bowling enabled Clark to remove Lumb but the sixth-wicket pair stood firm in fading light, with Patel reaching his 50 from 77 balls with seven fours.