I have received a *.lpk file from Esri's ArcGIS platform that I would like to convert to a shapefile.
How can I do this, using only free software?
I don't think I've ever seen this officially documented, but a layer package is a zip file that contains a .lyr file and a file geodatabase. You can change the file extension to .zip, unzip it and then, if the layer package was create with 10, read/export features to shapefiles using OGR.
LPK is a proprietary layer package (zip file) made by ESRI.
I stand corrected. See Zach's answer
Converting to shape file is another matter.
If the originating data is gdb then the resulting lpk unzips to a file gdb. HTH
In case you have ArcGIS installed, then open the LPK layer file in ArcMap. Select the layer and right click and then click "Data" menu item and then click "Export Data" sub-menu-item. You can select the format of the output file.