Part of the reason the Omaha channels are carried on cable in the Lincoln market, in areas like Lincoln, Seward, York, Beatrice, Crete, etc. is that until the mid-90s, Lincoln only had one local commercial station -- KOLN. Basically, Lincoln and the eastern half of the Lincoln/Hastings/Kearney TV market was just an offshoot of the Omaha market (plus KOLN as *THE* local station). Now the Lincoln market is more defined, especially if you consider the Tri-Cities signals available on satellite, but old habits die hard. 3, 6, and 7 all still have significant viewership in Lincoln. Plus there seems to be a thing about "larger market appeal" where some simply prefer the Omaha signals, thinking there's a more "big city" style (off-topic: not sure how anyone could think that about WOWT news of late) while the opposite would tend to be the case in Omaha. Many Omaha viewers would not likely choose to tune to a Lincoln station due to it being a smaller market. While certainly not applicable to all (I would definitely watch KOLN if it were carried on Cox) there exists among some in Omaha a bit of a disdain for anything outside the Metro...
Finally, the FCC "significantly viewed" list (which dates back to before KLKN signed on) is in play. Cable companies are expected to carry any channel that is on the county's significantly viewed list. Since it dates back to ~1994, that keeps all the Omaha signals on cable lineups. If a small cable provider only has room for one affiliate on each network, then KETV is carried as KLKN is not on the list (last I checked anyway, unless it has very recently been updated).
No Lincoln channels are on the significantly-viewed list for Douglas or Sarpy County. Not sure about Saunders and Cass either. Finally, I believe some of the Omaha stations have exclusivity deals with Cox. Back when there were disputes between Cox and a couple local broadcasters over signal retransmission, Cox had to drop the digital signal and wasn't allowed to bring in a Lincoln signal or national network feed.