For example, Can I calculate atomic density contour maps with LAMMPS, CHIMERA, etc.? Or, with any other MD softwares?
VESTA software can be used to visualize electron densities from DFT calculations, but it accepts a variety of volumetric data types. I don't know what the output files would be for your MD software, but you might consider checking out the accepted data types on pages 128-137 of the VESTA manual (see the first link). If it could be useful for you, VESTA can be downloaded at the second link.
http://www.geocities.jp/kmo_mma/crystal/download/VESTA_Manual.pdf
http://jp-minerals.org/vesta/en/download.html
The simple answer is none. As Martin said you can plot electron density contours but you should calculate it separately in any DFT code. Maybe some ab initio MD (AIMD) code could do this plot but certainly classical MD can't.
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