The second wing of LFR is open this week, so two pets are available from LFR now - Living Sandling and Ji-Kun Hatchling. I'm looking forward to collecting the hatchling first; it's so adorable!
Both pets should come as extra loot after defeating the last boss of each wing (Council and Ji-Kun). Players have reported receiving the "failbag" in LFR, an option to roll, as well as the pet. In normal mode, the Living Sandling comes from trash, but the Ji-Kun Hatchling is still a drop off of the boss of similar name.
I'm not sure if using your bonus roll will increase your chances of receiving one of these pets, but if you need the gear from either boss, it doesn't hurt to try. :)
According to Mumper, it is possible to keep running each LFR repeatedly just for the pet. His Tweet wasn't very clear, and at the time of his response I was under the impression you could get the Living Sandling from trash mobs, so it's still a little unclear if doing LFR multiple times a week will actually yield anything. But, again, if you have the time and/or a few toons that need the gear from LFR, it doesn't hurt to try. I know I'll be attempting both wings a few times this week for my toons!
Unless you get very lucky, don't expect to see either pet on your first few LFR runs. Mumper states that "it's low" (the droprate). Grats to those that get these pets though, and good luck to everyone still seeking them.