'They left this in the door' is decently common, at least if you live in area with two doors, one which isn't always locked. Like indicated above, sometimes people slip things "in the door" -- that is, they close the door on a flyer so it sticks partially inside and outside. I'm pretty sure I've heard this English phrase around the USA.
I may be incorrect, but you would use lo or esto, but not both, with slightly different meanings:
Ellos lo dejaron en la puerta - They left it on the door
Ellos dejaron esto en la puerta - They left this on the door
So using both would be like 'They left this it on the door'... at best redundant, at worst contradictory.
I agree, that lesson was a bit confusing. Check this link: http://www.studyspanish.com/lessons/dopro1.htm It really helped me. But basically, those words are a short way of saying it/him/her/etc.
What does "allowed in the door" mean? Are you using it to mean the equivalent of “allowed it to enter"? I ask because 'dejar' as 'to allow' usually goes with another verb (which is also often the case with the English 'let').
There is quite a difference in Spanish between dejar+ location (left at door, for instance) vs dejar+ verb (e.g. let me enter). “Me dejó en Memphis" is “he left me in Memphis" while “me dejó cantar en Memphis“ is “he let me sing in Memphis."
This was two years ago so I doubt you're still seeking an answer. However, for those who may still be perusing the forums--esto means 'this' but it refers to something that has no gender or when the gender is unknown; este is the masculine version for when you know the gender; and along those same lines esta is the feminine version.
Este es un boligrafo. (This is a pen -- boligrafo is masculine.)
Esta es una manzana. (This is an apple -- manzana is feminine.)
Esto es un gato. (This is a cat -- gato is the default option but you may add esto if you are unsure whether the cat is actually male or female.)
Esto es estupendo. (This is great -- stupendo is masculine but you are not sure what it is referring to.)
Or not. I'm just learning as well. :)