Not one of those terms you hear much anymore, “local-into-local” is a term that was used a lot in the 2000s when local channels on satellite were a fairly new thing. It wasn’t until 2000 that satellite services were even actually allowed to carry local channels, and so the race was on in the early part of the decade to add as many of them as possible.
As part of this rush, engineers needed a term for those channels that only served a local market. In other words, like your local ABC station. Legally, your satellite company could only deliver it to you and the area around you… they couldn’t deliver it to another market. This was in contrast to so-called “distant network” channels which could go into any market where they hadn’t added local channels. (Distant network channels usually came from New York or Los Angeles.)
So your ABC station was local to you, it only went into your local market, so they called it a “local-into-local” or “LiL” station.
Honestly, you probably never even cared how they did all of this, but they did it by using a spot beam to focus your stations on your local area, and an access card to make sure that even if you had a receiver from another part of the country you still couldn’t see someone else’s programming.
All of this fancy engineering was important because FCC rules (back when the FCC still had rules) said that your local network affiliate had the right to be totally exclusive in your market, and another station could be fined if their signal went into a market where it wasn’t supposed to go. There were exceptions to the rule but regular people really couldn’t get them.
Today, local programming is as important as ever, but it’s just not a new thing like it was in the 2000s, so people don’t use this term much anymore, even on the hard-core enthusiast forums.