What is the origin of "the lay of the land?"
The specifics are proving rather elusive. However, yourdictionary.com notes:
A related expression is how the land lies, as in Let's be cautious till we know how the land lies. This usage originated in Britain about 1700 as the lie of the land and is still so used there.
The modern definitions for 'lay' (or 'lie' for British English) do not include the meaning needed for this idiom, but must have at some point. That, or some other factor is needed to explain from whence the phrase evolved. The word which does fit the expression—layout—didn't turn up until 1910, according to etymonline.com. 'Layout' also implies a root definition for 'lay' that has been lost (well, transferred, anyway).
In the entry for lay, EtymOnline says that, in its verb form:
Meaning "way in which something is laid" (lay of the land) first recorded 1819.
The first written piece that Google turned up is a NY Times article from 1892, in which the phrase is also used.
Considering that the American frontier was still open during this time, it is still possible that the term originated because scouts were sent ahead to get the topology of a piece of land before settlers moved in. However, without citing a specific source I can't conclusively say whether or not this is true.