Is it possible to give digitized altitude lines (from paper map) heights using QGIS?
3D is not (yet) implemented in QGIS, but you can store the height in an attribute table field and create a 3D output manually with
ogr2ogr -z_field fieldname outside QGIS.
See Is it possible to create 3D dxf with OGR? for an example.
This is rather 2.5D, because all vertices of a line must have the same elevation (as contours have).
In QGIS, you could use
Save As ... and put into the layer creation option field
-SHPT=ARCZ according to http://www.gdal.org/drv_shapefile.html , but I don't know how to add the
-z_field option there.