We do know that there will be another wedding taking place at a different venue in the same building so that may have an impact on parking.

One option is the Midtown Parking Garage which is connected the Lumber Exchange Center and AC Marriott: 11 S 4th St, Minneapolis, MN 55401. Ramp entrances are located on both 4th Street and 5th Street (If coming in off 5th Street, you will need to cross over the light rail track at Nicollet). Access to the venue will be on the 3rd floor.

A cheaper option (but will fill up more quickly) is the surface lot across the street from the Lumber Exchange Center, directly below the Bob Dylan Mural, Downtown Auto Park: 509 Hennepin Ave, Minneapolis, MN 55402

You'll be able to enter the Lumber Exchange Building via the revolving doors you can see from the parking lot, beginning at 3pm. There may be a security guard stationed that this entrance.