Apparently I dropped down from the area I was transported to by Lilith and I cannot find how to get back there, so that I can get to the Bloodshot Stronghold now i'm lost. Is there another way to get there? Is there a way to find Lilith and ask her to transport me there again? Apparently I was supposed to stay where she transported me to and walk down the steps from that area where there is a trunk/chest and two lockers on the left. Not the area where there is the vending machines.
If you fell down from that path, then you've missed some loot, but that's it. You just need to go back to Sanctuary to continue the quest.
If you really want to go back to get the loot, you'll have to run all the way back the same way you came the first time.
Man, i encountered the same problem with one of my characters. Don't worry, it's actually part of the story. Lilith actually fails to teleport you, placing your character just a few meters away from previous position (her lair). Just go back to frostburn canyon and follow the mission indications, you'll be fine (..mission to the Dust, new car, bla bla...). In a couple of missions you'll be entering the Bloodshot Stronghold.
A little tip: before going in... level up. Quite a bit.
It is possible to jump to that platform from the side you start out on (on PS3 and PS4 at least). It isn't easy, and probably not worth it since there's only a chest and a couple ammo/cash boxes, but I have done it.