It would not be accurate to translate “fekszik” to “lie down”, because that would be better suited to “lefekszik”. “Lie down” and “lefekszik” both imply the transitory act of assuming the position of “lying” on a bed, for example. That is, a person cannot (or rather, should not) “lie down” for hours, nor can said person “lefekszik” for very long.
However, a person could “lie” and/or “fekszik” for as long as one might like, because neither are of transitory nature.
If it is hard to see the difference between “to lie down” and “to lie” (because they are often used interchangeably), look at the transitory nature of the verb “get up”.