I think I'd personally never say "Kaffen ligger […]". I'd use "står", possibly "er". – Mostly because I never imagine coffee to lie. When referring to the coffee, one often mean the container that holds it. I imagine such containers to be open, and don't expect them to lie. For other objects it is perfectly natural to use ligger.
I've seen references to such things as "notes" [for a lesson] and now the "introductory screen for this topic", yet I haven't noticed anything like this for any of the lessons. Am I missing something? The lessons just jump directly into the quiz questions. I'd welcome a little explanation first!
It's very easy to mix up the verbs 'lay' and 'lie', but one way to keep them apart is to remember that 'to lay' (å legge) requires a direct object, while 'to lie' (å ligge) does not take a direct object.
In this case the coffee is the subject of the sentence, so it's just lying there on its own - it's not an object that someone is laying anywhere.
PS: Beware that the past tense of 'to lie' is 'lay'.
it's not the most natural with coffee in particular, but you could certainly say something like 'the book is lying [or laying] next to the tea'. I think there's something weird going on in English where objects that are lying need to have some particular quality, maybe that they're flat? like, 'the tea bag is lying there' is a bit more natural than 'the tea is lying there.' Something really idiosyncratic like that.
There's also a thing going on, I think, about where English uses 'lies' vs. 'is lying.' Since Norwegian doesn't have this distinction, it ends up being a little funny to translate sometimes.
Sorry, but I'm afraid you are mistaken. In English, "lie" is an intransitive verb, used for animals, objects, and people. "lay" is transitive, meaning "to cause something to lie". Example: "I lay the coffee on the table. The coffee now lies on the table."
Confusingly, "lay" can also refer to the past tense of "to lie". The past tense of the above example would be: Example: "The coffee lay on the table yesterday, after I laid it on the table."
More information: http://grammarist.com/usage/lay-lie/