As things stand now, the Academy Museum is slated to open in 2019 and the Lucas in 2021. But big museum construction projects never open on time. The Academy Museum's opening has already been pushed up from 2017. The odds are the Lucas timeline will slip too.
Dickey's premise is that the Academy Museum is facing stiffer headwinds than the Lucas is. The Lucas has a single client to please, and he's putting up all the money. The Academy must placate many stakeholders, most of them egotistical. Fund-raising has stalled while the budget has increased from $250 million to $400 million. This past April Variety quoted an unnamed "Academy insider": "We are really concerned right now that we won’t have enough money. This could be a catastrophic situation."
So it's not inconceivable that the Academy Museum could lose most or all of its two-year lead on the Lucas. The worst-case scenario for the Academy Museum might be to open just after the Lucas. "Movie museum? Another one?"
(At top, a bit of narrative art from the Lucas collection: John Phillip Falter's Sunday Gardening, 1961.)