Is there any way to get contour lines wth OpenStreetMap's Overpass API? I can see them in the cycle map - but I can't seem to get this data at all through Overpass.
There is NO way to get contour lines with the Overpass API.
Overpass API only has access to the OpenStreetMap Server, and that contains no dense elevation data to create contour lines.
The contour lines in the cycle map of openstreetmap.org are generated from elevation data of other sources, like SRTM, Aster or else. The author does not reveal much about the styling of his map.