The 23-year-old sprinter claimed victory after coming home second for the second time this weekend, and again at the end of a bruising day of racing.
He was beaten to the line by defending champion and Olympic gold medallist Greg Van Avermaet of CCC, who added to the overall win in 2018 with a first stage win at the race.
On a thrilling final stage from Halifax to Leeds, World Tour heavyweights Chris Froome and Van Avermaet traded blows on Otley Chevin as their respective teams Ineos and CCC jostled for the overall victory.
Then Van Avermaet launched his bid for a second successive victory from 6km out but found himself sandwiched by the young Ineos duo of Eddie Dunbar and Lawless.
Van Avermaet won the stage but overall honours and the blue jersey at the end of a thrilling 'Yorkshire Terrier' stage.
"For a start for Ineos, we couldn't have asked for much more," said Chris Froome, who served as a domestique for his younger team-mates, Dunbar and Lawless.
Lawless said: “To have my first GC win at a home race is unbelievable.“I never expected to be that far up on GC, let alone win it. I surprised myself and I’m a little shellshocked.”