The Falcons lost out by 30 runs.
Lancashire won their fifth successive Royal London one-day Cup game to close in on a top three finish in the North Group and knockout qualification, with Derbyshire soundly beaten by 30 runs at Emirates Old Trafford.
A two-hour rain delay forced a 38 overs per side contest on a used pitch, which made acceleration challenging.
Australian overseas debutant Jake Lehmann’s unbeaten 77 off 67 balls was the feature of Lancashire’s 239 for six before the Falcons were tied down against spin and finished on 209 for seven.
It means Lancashire sit second with 10 points from seven games ahead of their final outing at Warwickshire on Saturday.
The Red Rose last achieved this winning streak in 2013 when they won six 40-over games in a row. They last reached the knockout rounds of a List A competition in 2012.
Derbyshire, who have seven points from seven outings, may be out of contention by the time they wrap up the group stage against Worcestershire on Monday.
Steven Croft was the pick of the home bowlers with two for 20 from seven overs of off-spin, while Rob Jones and Matthew Parkinson also struck.
Lancashire’s innings was underpinned by fourth-wicket pair Keaton Jennings’ 84 off 88 balls and Lehmann, both of whom were measured as they shared 86 in 14 overs after Derby won the toss.
Haseeb Hameed and Croft, stumped off Wayne Madsen’s off-spin and caught in the deep off ex-West Indies seamer Ravi Rampaul, departed to leave the score at 42 for two in the eighth over.
Jennings and captain Dane Vilas (25) shared 52 for the third wicket before the latter mistimed Luis Reece’s first ball of medium pace to short cover - 94 for three in the 17th.
Then came the key partnership between left-handers Jennings and Lehmann, who has replaced compatriot Glenn Maxwell for the remainder of the RL50.
Lehmann swept Rampaul over long-leg for his only six and posted a 48-ball half-century, a milestone Jennings had earlier reached off 57.
Jennings, on 29, was the subject of a disputed caught and bowled effort from leg-spinner Matt Critchley.
Jennings fended a short ball from New Zealand overseas quick Logan van Beek behind at the start of the 31st over as the hosts slipped to 180-4 before Jones and Josh Bohannon fell to Scotland international Mark Watt late on.
Left-arm spinner Watt (two for 50 from eight overs) represented Lancashire in last summer’s T20 Blast.
Lehmann paced his innings nicely even though Watt and co limited any late damage.
Lancashire fast bowler Liam Hurt fell awkwardly as he attempted to launch Watt for six in the last over, retired hurt and later did not take the field.
However, that forced the use of extra spin from Croft and Jones, and they were key in stifling the visitors, who slipped from 46 without loss in the 10th over to 122 for six in the 27th.
Reece and Alex Hughes were run out, while sandwiched in between Madsen was caught at long-on off Jones’ leg-spin and Croft had Billy Godleman caught and bowled off a full toss for 42 and Tom Lace lbw, pulling, four balls later.
When Parkinson had Critchley caught at mid-wicket, it was virtually game over with Derby six down.
Anuj Dal played the day’s most aggressive innings with 52 off 39 balls, but he had been left with too much to do and edged Graham Onions behind. Onions was left defending 35 off the last. Harvey Hosein was 41 not out.