"a (usually luxurious) apartment situated at the top of a tall building"
This is very much a modern meaning, first recorded in the 1920s, in the age of high-rise buildings. Shakespeare uses the word only four times, but the sense is rather different. "Stand thee close...under this penthouse", says Borachio to Conrade (Much Ado About Nothing III.iii.101). Under a penthouse? All becomes clear when we know that in Early Modern English the word referred to a covered way, usually a sloping porch or overhanging roof. Gratiano uses it to Salerio: "This is the penthouse under which LorenzoDesired us to make stand" (Merchant of Venice II.vi.1). The other two uses are metaphorical, both emphasising the vertical: Mote describes Armado's hat as resting "penthouse-like o'er the shop of your eyes" Love's Labour's Lost (III.i.16). And the First Witch uses it in cursing a sailor, forbidding sleep to "hang upon his penthouse lid (Macbeth I.iii.20 ). Fine images, indeed.
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin