With her first three headlining tours:
The Monster Ball
Gross: $227.7M
Average: $1.120M/night
Born This Way Ball
Gross: $181.1M
Average: $1.845M/night
artRAVE: The ARTPOP Ball
Gross: $83.04M
Average: $1.122M/night
Cumulative gross for first three headlining tours: $491.54M ($504.8M in total 2014 dollars)
EDIT: This total excludes Roseland Ballroom gross of ~$1.5M and the unknown totals for The Fame Ball, many shows from which were fee-based as Gaga wasn't headlining the event and so wasn't responsible for the gross. It also obviously excludes unreported dates from artRAVE (Sweden is unreported, as are the festival stadium shows in Canada, Atlanta and South Korea).