"The entrance lies to the north" isn't accepted, but it suggests "lay" as a possible answer. Maybe this is an American thing, but 99% of native English speakers don't know the actual difference between lay/lie when talking about the position of objects. Both should be accepted.
"lies" isn't accepted because it is present, while the German sentence uses the past ("lay" is the past of "lie", and you can see that this is how it's being used from the fact that it isn't "it lays" as it would be if the verb "to lay" were being used). I also think you are grossly overestimating the percentage of people who don't know the difference.
I don't agree that such errors should be accepted because it is a non-standard usage that is completely inappropriate in formal speech, it has no place in a language learning tool that can use the standard definitions and differences in the base language to―for example―explain differences in the target language, like the corresponding legen-liegen distinction. Furthermore there is a number of German speakers who use the English-to-German section to improve their English and it wouldn't be fair to confuse them with non-standard usage.
The difference between "lie" and "lay" is, in my opinion, worth learning:
"lie" is intransitive and simply indicates the position something/someone is in. E.g.: "I was lying on the bed", "the cat is lying on the floor". It can be used with "down" to indicate that one goes from another (sitting or standing) position to a lying position: "I am going to lie down". Past simple: lay, past participle: lain.
"lay" is transitive and means putting something in a lying position. E.g.: "lay down your weapons!", "she laid the baby in his cot". Past simple and participle: "laid".
In general, if there is an object it's always "lay", otherwise it's "lie". So you can't "lie it down" and you cannot "lay on the bed", but you can "lay it down" and "lie on the bed".
I don’t disagree with you entirely, but there are many, many counter examples (at least in common American speech) that go against your bulleted guidelines. For example, if you want to tell someone to take their place on a bed or couch—which is transitive—you’d say “lie down”. Another common phrase for the same thing is “go lay down”… so now we’re
I do think it would be nice if everyone learned the simple rules that you laid out (or is it "lied out"
"Taking one's place on a bed or couch" is intransitive: you can't "take your place" someone or something, it can't have an object; "lie down" is indeed the correct phrasing.
Interestingly, I have heard people using "lay" where "lie" would be standard, but never the opposite. Do you find the same? (I ask this out of curiosity, living in a non-anglophone country and having ultimately very limited contact with native English speakers, much less of the American variant)
We can agree to disagree. We probably have different opinions on what makes a usage "standard" or "acceptable" anyway. Still, I must note that the Merriam-Webster dictionary considers "lay" as a non-standard variant of only sense 1 of the word "lie", excluding the meaning "to occupy a certain relative place or position" (the acceptation used here); but I suppose the main reason for that is that the informal speech that would allow "lay" for "lie" would hardly ever use "lie" in the latter sense.