How do you restart the Boeing 787 in mid-air? With the lack of an APU (they use li-on batteries, I think?), what's the mid-air engine restart procedure?
Just like any other jet enige... Get it to spin fast enough, enable the igniters and add fuel. Be careful with how fast they spin before adding fuel, too slow and things get very hot and melt.
Getting them to spin fast enough in a 787 is a bit different from a traditional jet engine, because traditionally you spin them by pneumatic power (from ground, APU or the engine) and in the 787 you spin them by electric power (from ground, battery, APU, other engine or RAT). But there isn't much difference from a pilot's point of view.