Too much trouble, better to take the train from Beijing.

From Beijing to Lanzhou by train: 9:30pm -> 4pm next day.

By flight: go to airport, waiting to check in, flight + possible delay, from airport to Lanzhou city, go to the train station ==> at least 7 hours, and you have to get up early, and counting delay ==> better take the train from Beijing.

If you want to spend some time in Lanzhou, that is different story.