LFG is an abbreviation for "Looking For Group", commonly used by players in towns and outposts desiring to join a party working on a mutually agreed mission, quest or any other objective (often followed by the objective's name, like "LFG Blood And Smoke" or "LFG farming for IDS"). Players often include their build in order to receive invites from teams looking for that particular specialisation (eg. "Interrupter LFP").
The abbreviation "LFP", for "Looking For Party", has the same meaning. Note, however, that it can also mean "Looking for Player", in which case it would be the equivalent of GLF.