"She lies down."
Translation:Hun lægger sig ned.
OK that is clear as far as the Danish expressions. Then I think the best translation for"Hun ligger ned" is "She is lying down." I don't hear "She lies down" much. If you want to include the word "down" it's usually in the expression "she lays down. The most natural translations of "Hun ligger ned" will be "She is lying down" or ""She is lying (on the bed)."
It is as tddk has pointed out, but one can't say "hun ligger sig/sig ned". Instead, this becomes "hun lægger sig/sig ned".