IMO and with my personal experience of raising two children plus being very close to lots of other children (nieces, nephews, children of close friends) and with having worked with children from violent homes for over 20 years, no. Not every child threatens or attempts to run away from home at some point or another. I am sure it never occurred to my kids to run away from home. In fact, we talked about it and they couldn't understand why a child would want to run away. My kids loved being at home. Even if things weren't going their way (which was often) they would cope without wanting to leave. But I do not think it's necessarily a reflection of a "troubled" child. And, I don't think all children who do have more than their share of difficulties do think about running away from home.
I think that some children sometimes feel a little lost. Threatening to run away, not actually running away, is sometimes a way of asking for reassurances. It sounds like Lyric's grandmother gave Lyric the reassurances that she needed and that was the end of it. She was late coming home 3 days before she vanished and the family was on the phone with police when she walked in the front door.
I wondered if she met someone four days earlier when she was late returning home with her 11 year old cousin. I guess nothing panned out with the cousin ... no conversations with strangers that offered a lead. If the cell phone, computers and recent outtings make no connection with a pre-arranged meeting, then this looks more like a random crime of opportunity ... wrong place, wrong time.