Marcus’s Train, Digistruct on OP8, WEP…depends on the gear your looking for.
My best luck with legendary shields & grenades has always been the Train.
Is that so? Do they drop things other than class mod and grenades? That’s all the train drops, apart from legendary pistols from time to time.
Do I have to open up lockers and shoot skag piles or do they spawn while I’m fighting enemies?
The LLM’s in WEP can drop Legendary and some Pearlescent weapons in edition to Grenades and other items. Just make sure not to pick up any of the Notes (at least not more than 1) for the Doctor’s Orders mission. Also, it is possible to get other Legendary (or even Pearlescent) Weapons from the Loot Train. I have gotten Legendary Shotguns and Sniper Rifles in addition to Pistols, Shields and Grenade Mods, etc.
Forum ID: Poisd2Strike
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Gun Prefixes | Gun Parts | Max Stats
Maya OP8 | Banshee RR / NRR | Binder | Cat | Nurse | Siren | Trickster B / M
three specific boxes, all in one spot.
Are you talking about the room on the right before the area where you see that bloodwing isn’t there?
Just saw a video saying that.
indeed
One of the Doctor’s Orders Notes is in one of the 4 small cardboard boxes in that room. There is a Red Chest on the opposite side of the room. You have to be careful not to pickup the Note, by mistake, when opening the small cardboard box.
Forum ID: Poisd2Strike
GT: Poisd2Strike
Trades: http://forums.gearboxsoftware.com/t/poisd2strikes-humble-shop/367700
Gun Prefixes | Gun Parts | Max Stats
Maya OP8 | Banshee RR / NRR | Binder | Cat | Nurse | Siren | Trickster B / M
but do open it, because sometimes there’s 4 LLM’s.
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The fast and informative replies are much appreciated. 
the video I saw, though, the guy had the “wildlife preserve” mission active and not the doctor’s orders one. Should I just stick with the doctor’s orders one? This guy got a bunch of midgets to spawn, whom also dropped several pearls as well.
It is a good idea to have Doctor’s Orders active, if for no other reason than to see how many Doctor’s Notes you have picked up. Ideally, you want it to say 0/4 meaning none have been picked up. Another good farming area is Thousand Cuts with Rocko’s Modern Strife Active. Don’t turn it in by speaking to Rocko. While it is active the enemy spawns in Thousand Cuts are greatly reduced (including Buzzards), allowing you to farm containers for LLM’s without having to worry about being attacked too often.
Forum ID: Poisd2Strike
GT: Poisd2Strike
Trades: http://forums.gearboxsoftware.com/t/poisd2strikes-humble-shop/367700
Gun Prefixes | Gun Parts | Max Stats
Maya OP8 | Banshee RR / NRR | Binder | Cat | Nurse | Siren | Trickster B / M
unless im going for specific loot (norfleet from hyperious for example) i love doing the LLM run in WEP, and since i have the natural selection annex, i can cut the time to farm the LLMs in half since you start halfway through the map when doing a start/quit after farming the 4 boxes in that room, tho, my fav. drop ever came from the bunker right after finishing tvhm and was looking for a sham, he dropped a level 49 shock infinity after id spent i dont know how long trying to farm doc mercy for any infinity at all, lol
to add, if you’re above level 61, doing tubby runs in the dust for tubby spiderants behind ellie’s is another of my favorites (the run to get to the end of the quest, the good, the bad, the mordeci)
You guys rock. I had no clue LLM spawned in the wildlife area. I used the selection annex method as well to cut my time in half. Been farming since 10 PM and now it’s 1:30 AM and I got 5 pearls and I think around 7 legendaries. Pretty good run if you ask me. Although, the pearls look really really crappy. I got the unforgiven, two butchers, that one sniper rifle, and that one rocket launcher. I already had a stalker from Marcus’s train.
I am now just missing the avenger, sawbar, and bearcat. Going to continue farming tomorrow. 
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I generally farm behind and in front of Ellie’s garage for tubbies. Also, Frostburn Canyon tends to have LLMs that’ll pop out of the various lockers and ammo crates; I’ve even had a few pop out of the crate by the machines outside of Lilith’s hidey-hole.
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I usually go into the Treasure Room. Then WEP and Sawtooth for LLMs, Arid Badlands for tubbies.
For general purposes the Loot train, for specific stuff Dragon Tower (for Magic Missiles, Tiny Tina class mods and Handsome Sorcerer drops), Lair of Infinite Agony (Chain Lightning/Firestorm) the Dust (tubbies, Slagga, Veruc and White Death), Arid Nexus Badlands and Boneyard for tubbies, WEP for the LLM and Lynchwood just for the hell of it…
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I’ve gotten just about every gear type under the sun in Legendary and sometimes Pearl rarity from the train. As with everything else in the game, it just comes down to luck.
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the train hates me.
My fav place to farm is Master Gee, but it’s because I’m a masochist…and I’m absolutely kidding.
I once got 10 LLM’s in a row in Sawtooth. TEN.