is it just me or does lagde sound a bit like laid
To me, it sounds more like "lay," but close enough to "laid" to make you think of the English cognate, like so many of these words that SOUND much more familiar to the English speaker than they LOOK.
Which also confirms that the pronunciation given at ordnet.dk does not reflect how Danes speak today! ordnet.dk gives: [ˈlæː]! This is far from reality.
In German one would say "legte" which means laid. I think the words have the same origin.
Why not placed?
Would "laid" not be a correct translation here?
It is and it is accepted.
Should "The woman placed the dress on the bed" also be accepted?
Seems like "placed" is a synonym of "put" in this case, and I've seen it accepted in other sentences.
I think "kvinden satte kjolen på sengen" works better here.
Could a Dane confirm this?
You would say "Kvinden satte kassen på sengen", but I doubt that in Danish a dress can "sit" in the way a more solid object (e.g. a box) can.
On reflection, I now understand that "lagde" is correct for this sentence as a dress doesn't have a natural upright / standing position.
Laid on the bed is more accurate english.