"She swam across the whole lake."
Translation:Ŝi naĝis trans la tutan lagon.
Direction is being indicated though. Compare saying that something is across the lake (Ĝi estas trans la lago.) and that you swam across the lake (Mi naĝis trans la lagon.): In the first, there is no motion/direction involved, so no -n, but in the second, motion/direction is involved, so the -n is needed to indicate that, even if it's quite obvious what you mean with or without the -n. Hope this makes sense!
(Still a beginner though, so someone more fluent please correct me if I'm wrong!)
Of course, that makes sense, thanks. Just me having a silly moment, I think, born of thinking of the direction marker still as an accusative marker, which to me gives the feeling that the direction needs to be specifically into / towards / at, etc.