The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Los Angeles and Louisville. From the farther side that’s about 24 hr 43 min of driving.
Recommended midpoint
Oklahoma City, OK
From Los Angeles
24 hr 43 min
1,178 mi to Oklahoma City
From Louisville
14 hr 12 min
677 mi to Oklahoma City
Louisville has the shorter trip; the split is off by about 10 hr 31 min. The alternatives below can even it out. Los Angeles and Louisville are about 1,826 miles apart.
Los Angeles and Louisville are about 1,826 miles apart by road. Split the difference and you arrive near Oklahoma City, the city closest to the halfway point between them. That puts roughly 24 hr 43 min of driving on the Los Angeles side and 14 hr 12 min on the Louisville side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Oklahoma City still makes a fair, central place for Los Angeles and Louisville to converge, splitting the travel instead of asking one side to cross the country.
If Oklahoma City doesn't have what you're after, Albuquerque and Denver are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Los Angeles and Louisville.
Oklahoma City, often shortened to OKC, is the capital and most populous city in the U.S. state of Oklahoma. It is the 21st-most populous U.S. city and 8th largest in the Southern United States, with a population of 681,054 at the 2020 census. Read more →
Los Angeles (LA) is the most populous city in the U.S. state of California, and the commercial, financial, and cultural center of Southern California. Read more →
Louisville is the most populous city in the U.S. state of Kentucky, sixth-most populous city in the Southeast, and the 27th-most-populous city in the United States. Read more →
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.
Estimates use straight-line distance and typical road speeds; real drive times vary with route and traffic.