It depends on the location and technology. For example, if an LG phone model has a G in the model number, it's a GSM phone and it will activate on either AT&T or T-Mobile, depending on the location. If the GSM phone was purchased in Puerto Rico, then it would probably activate on Claro, which is also owned by TracFone's parent company.
If the LG model has a C in the model number, then it's a CDMA phone and it will activate on Verizon, US Cellular, or perhaps a smaller CDMA carrier, again, depending on the location.
America Movil/Straight Talk/TracFone customer since 2004.
verizon customer since 2012.
T-Mobile customer from 2005-2014.