Break the name down: "lg dms client att". I assume that the phone is an LG handset ("com.lge" is a giveaway). That in itself tells you that this app is from the manufacturer of the phone. "DMS" is ambiguous: "device management", "download manager", "digital media" are all possible. "Client" is standard software jargon, it just means something that's using a service. "ATT" is obviously your service provider. So while the "DMS" is ambiguous, putting together the "LG" and "ATT" it's obviously something that the phone manufacturer has added to customise the device for the service provider. Basically this is not something your daughter is running herself, it's just one of dozens of processes that runs in the background in order to make the phone work. Any phone's activity log will be full of this sort of stuff no matter what the user is doing.
I'm not sure I'd trust the Google source that said that this is something to do with an ATT phone calling a Verizon phone though: there is no reason for the phone to know or care what network the person you are calling is on, that stuff is all handled by the network rather than the handset, so that explanation seems extremely implausible to me.
