If you select all the parts you want to export in viewer and choose export dxf file or export dxf with layers this should export the parts with overlaying lines also

by the looks of your screen shot you have exported the dxf parts from a nest which will not export the other lines

also note that dxf file export will only do a qty of 1 so if you have a qty of more than 1 on any of the parts then you need to duplicate these manually

screenshot below of how I export them

hope this helps