Cursed by my own English shortcomings by saying "lay" instead of "lie". 19 and I still never do that right.
I'm going to take a shot at freeing you of this particular grammar curse: Lay: to place or put something down. Lay is transitive and takes a object. Lie: to recline. Lie is intransitive and does not take an object. Example: I lie down. (no object) I lay myself down. (myself serves as the object) The ball is lying on the table (ball is the subject, not object) I lay the ball on the table. (ball is the object). When my children would jump on the bed I would say, "Lie down, before I lay you down!" - but I never did make them into direct objects! ;-) Hope this helps.
Got that wrong too. In other exercises "ligger" is translated as "is" just as sitter or står, but I guess it only works for objects.
The verbs "to lie" and "to lay" are essentially merged in colloquial English—the core difference being only that one was transitive and the other intransitive—so "Who is laying next to me?" should probably be accepted as an answer as well. This lesson is about teaching Swedish, not formal English, after all.
Just because people misuse them colloquially does not make it right. Lay is either 1) something you do TO something else or 2) the past tense of lie. Period. Lie is either 1) resting or reclining, or 2) telling an untruth. Lie/lay are in our 6th grade grammar curriculum.
It's in the curriculum because it's not something native speakers learn naturally. Descriptively, on this question the input available to a learner is so chaotic as to be useless, as the great Geoffrey Pullum wrote here: http://itre.cis.upenn.edu/~myl/languagelog/archives/000877.html