Here is the language as it appears on the OneWorld website:
Indulge yourself before departure in a wider range of airport lounges when you fly First Class or Business Class with any oneworld member airline, though exclusions apply. Customers flying First or Business Class have access to the equivalent class of lounge regardless of their frequent flyer status. First Class passengers may use a Business Class or frequent flyer lounge if a First Class lounge is not available. First Class passengers may invite one guest to join them in the lounge. The guest must also be travelling on a flight operated and marketed by a oneworld airline. Access is available on the day of travel (or before 06:00am the following day), at the airport from which the oneworld flight on which the eligible customer is travelling departs.
Connecting between oneworld marketed and operated flights: First and Business Class customers connecting on the same day of travel, or before 06:00am the following day, can access the lounge when travelling between an international long haul (a oneworld international long haul flight is defined as an international flight marketed and operated by any oneworld carrier with a scheduled flight time longer than 5 hours) and an international short haul or domestic flight (and vice-versa).
There are actually 2 different 6 am rules.
The first one govens
departure airport access. This means you can access a lounge at LAX if you show up at 8pm for 1 am LAX-HKG CX flight. Because the flight is before 6 am.
The second 6 am rule applies on arrive to the
connecting airport. It does not apply to the originating airport. There is no way to enforce this at originating airport because of time zone difference, many connecting flights would depart after 6 am local time at the departing airport.
In the example someone brought up: LAX-DFW-XXX... I actually have done this many times e.g. LAX-DFW-HKG. The first 6 am rule on departing airport would apply if the redeye flight departs after midnight. So if I show up at 10 pm for 12:30 am LAX-DFW, I'm granted lounge access (even if it is in Y as long as DFW-HKG is J or F). This flight would land in DFW in the morning so the second 6 am rule wouldn't apply.
Now let say I have a LAX-JFK-LHR itinerary with a 12 hour layover. The second 6 am rule would kick it once I land at JFK. LAX-JFK departs 12 noon and gets in at 10 pm but my JFK-LAX is next morning at 10 am. I could have lounge access at LAX if this is a 3-class J boarding pass but when I get to JFK, they would tell me to go find a hotel and come back in the morning.