This expression, exactly as used by OP, is ubiquitous in the south eastern U.S. I concede that, linguistically, the region is more anglophile and more conservative than most of the U.S., but claiming it is just a U.K. regionalism is just plain wrong. The "informal" part, I'll buy.
I've lived in the US SE for 50+ years - I've never heard this saying. A quick check of those living in this home (all whom have lived in the SE all their lives) and none have heard this either. So I don't know that "ubiquitous" is the proper word here.
I've lived in Virginia, North Carolina and Florida. Which SE US are you referring to? Tangier island?
East Texas east through middle Georgia. The Branford/Fort White of north Florida. Haven't spent enough time north or south of that belt to be sure about those dialects. Yes, the states you mention are certainly southeastern. Maybe I should have said "In the heart of Dixie." I hear it frequently, use it myself, and never encountered anyone who didn't seem to understand it. It is obviously related to "look out" as a verb. As in, "Just past the dam, you gotta look out for cops." And to a slightly different use as a noun such as "If you go that way, you'd better keep a good lookout for cops." Now, dammit, you got me overthinking it, and next time I write it I won't know whether to make it one word or two. Like the story about the man with a long beard. Okay, lessee . . .
My Compact OED, 1971 edition, has this meaning as sense 4.b. without any qualifying label at all, not regional, not even "informal", and gives 3 examples, 2 from fiction, and one from what apparently is a law journal or maybe text. I'm not going to transcribe those because the text is painfully tiny (That's what the "Compact" part of the title means - this is the full OED). All 3 examples are from the 19th century. Damn. Now I have 3 ways to spell it. The lawyer uses a hyphen.
Then there is this online, also from the Oxford University Press:
lookout | Definition of lookout in US English by Oxford Dictionaries
Home North American English lookout
Definition of lookout in US English:
lookout
noun
. . .
1.3 informal
A person's own concern.
‘everyone's life is his own lookout’
1.4 British informal in singular
Used to indicate whether a likely outcome is good or bad.
‘“What if he gets sick?” “It's a bad lookout in that case.”’
So they label this specific usage as U.S. usage, NOT as British. According to those chaps (and I reckon the editors live over thar 'crost the water) there is also a British informal usage but that means something else, NOT the sense OP asked about, but more what most Americans (ok, ok, most Americans I've known. The sheep may be black on the other side) call "outlook". Well. Those silly electronic-eavesdroppers - why don't they learn to speak our language?
OK, Cambridge says it British. Oxford says it's American. We should put gloves on 'em and let 'em fight. Oxford and Cambridge - that there's a grudge match kinda like Auburn and Bama, right?
OK, lets settle this business with an American dictionary from the civilized hemisphere:
The online version of The American Heritage® Dictionary of the English Language, Fifth Edition copyright ©2018 by Houghton Mifflin Harcourt:
The American Heritage Dictionary entry: look out
look·out (lkout′)
n.
. . .
4. South Atlantic US Outlook; view.
5. An object of concern or worry: "They were out of money. Of course it was her lookout to earn some" (Shirley Abbott).
Ms. Abbott, that's "Shirley Jean Abbott Tomkievicz", to be precise, comes from Hot Springs, Arkansas, which for y'all British folks is part of the South East. She is best known for autobiographical americana such as "Womenfolks: Growing Up Down South".
Well, that's interesting. I'd tend to pay more attentiion to AHD on the details of current American regional usage. Sounds like people along the southern part of the Atlantic coast follow a usage also common in parts of the UK, meaning prospect, prognosis, predicted events, what most of America calls "outlook". I wonder if the TV weather people there talk about "the lookout for tomorrow". For folks from the old world, those 3 states Onyx mentioned having lived in are all southern Atlantic coastal states. Whereas outside the Atlantic coastal area, the rest of us Yanks (not Yankees, please. That's different.) - well, if we have an outlook for tornados in the morning, that's our lookout - we'll just post a lookout at the overlook to look over the valley & look out for them twisters to make sure we don't overlook any.
Cathbad didn't say whar he was from. Maybe near the coast? Or that there Tangiers place? Or maybe we move in different circles. Maybe mah neck's redder than his'n.