Nineteen-year-old Lawless had escaped in the final laps of the race with Will Bjergfelt (SportGrub Kuota), and the pair worked well together to distance the chasing peloton.
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Steele Von Hoff (NFTO) brought the bunch home for third place.
Madison Genesis took the team win on the night to successfully hold off close rivals One Pro Cycling.
Television highlights from the Barrow round will be shown on ITV4 at 9pm on Sunday May 31, with a repeat at 8.25am on Monday, June 1.
The 10-date Tour Series continues on Tuesday, June 2, in Cycling Weekly‘s hometown of Croydon, which also hosts round three of the women’s Matrix Fitness Grand Prix series.
Pearl Izumi Tour Series 2015, round six: Barrow, Cumbria
1. Chris Lawless, Team Wiggins
2. Will Bjergfelt, SportGrub Kuota
3. Steele Von Hoff, NFTO
1. Madison Genesis
2. One Pro Cycling
3. Pedal Heaven
Pearl Izumi Tour Series standings after round six
1. Madison Genesis, 75pts
2. One Pro Cycling, 72pts
3. Pedal Heaven, 61pts
4. NFTO, 50pts
5. Team Raleigh GAC, 49pts
6. JLT Condor presented by Mavic, 37pts
7. SportGrub Kuota, 36pts
8. Velosure Starley Primal, 36pts
9. Team Wiggins, 16pts
Video: Quick-fire core routine for cyclists