Using Layer & Map Packages outside of ArcGIS

How to use ArcGIS Desktop layer and map packages if you don’t have ArcGIS?

Hopeful

Find someone with ArcMap/Pro to use Feature Class to Shapefile geoprocessing tools on the file-gdb contents within the package.

Self serve

Layer and Map packages (.lpkx, .mpkx) are a zipped up archive of an Esri file-geodatabase and some metadata to help with style and symbol display. For a non-Esri product:

1. Use 7zip or similar to extract into it’s raw components.
2. Drill down until you find something.gdb. This is the data. Everything else is for ArcGIS and can be ignored. There will be more than one copy of the same thing in different folders. You only need one. The naming convention goes like:
   • p12 is designed for ArcGIS Pro 1.2
   • p20 is designed for ArcGIS Pro 2.0
   • etc.
3. Use global-mapper, qgis, GDAL Utilities, etc. to read the file-gdb contents and export to shapefile or something else your other software can use.

As another option, there’s probably way to use a free public arcgis-online account to upload, add to web map, and then extract the data.

nb: credit to @derekswingley for the critical insight of this answer.