The Chicago music event evacuated tens of thousands of concert-goers to parking garages for around three hours until the storm had passed.
An extended curfew allowed Red Hot Chili Peppers to perform their headline slot as scheduled.
The Temper Trap and US rock group Alabama Shakes were among the bands whose sets were cancelled due to the interruption.
Calvin Harris tweeted: "Watching a huge thunderstorm from my hotel room on 43rd floor in Chicago...my lollapalooza slot is definitely in jeopardy."
He later added: "The storm has passed and my Lollapalooza set time is now 7:45!"
In a statement on their website, organisers said: "In all, more than 60,000 festival-goers and nearly 3,000 staff, artists and vendors were safely evacuated in 38 minutes.
"We want to thank the tens of thousands of festival-goers, staff and artists who calmly and safely exited.
"We applaud and thank the City of Chicago for their cooperation and commitment to making Lolla a safe and enjoyable experience for all. We look forward to seeing everyone tomorrow for one more day of rock."
Jack White, Miike Snow and Florence + the Machine were scheduled to perform at the festival today (August 5).
Lollapalooza Festival organisers recently announced that they will hold an event in Tel Aviv, Israel in August 2013, in addition to Sao Paulo, Brazil in March and Santiago, Chile in April.