Walk, Bike, L-Train, Bus, Uber
No, there is no official transportation sponsored by Lollapalooza.
There is no other music festival I recommend utilizing public transportation or walking for more than Lollapalooza. Given the festivals fantastic location at Grant Park in the heart of Chicago there really is no reason to go by car to Lollapalooza. If you are staying in Downtown Chicago more than likely you can simply walk or bike to the festival. If you are outside of walking distance you most certainly can use the train to get to Lollapalooza. Grant Park is right within The Loop so you can take nearly any L-Train to somehow get to the festival. Each ride on the L-Train will cost you just $2.25, making it economical as well as efficient. I really recommend against Uber as the traffic leaving Lollapalooza is absolutely abysmal and the prices are surged dramatically. Save some money and get to Lolla by foot or train.
$2.25 per ride on the L-Train. Chicago also has a bike share program (Divvy Bikes) with locations throughout the city that you can use for just $9.95 a day.
No, there is absolutely no parking available at Lollapalooza or Grant Park. There is parking throughout Chicago obviously, but expect increased rates ($30+ a day) for Lollapalooza.