The Makefile.lammps file in this directory is used when building
LAMMPS with its PYTHON package installed.  The file has several
settings needed to compile and link LAMMPS with the Python library.

The default Makefile.lammps will automatically choose the default
python interpreter of your system and will infer the flags from
the python-config utility, that is usually bundled with the python
installation. If needed, you can copy one of the other provided
Makefile.lammps.* files to to Makefile.lammps before building
LAMMPS itself.

The files Makefile.lammps.python2 and Makefile.lammps.python3 are
similar to the default file, but meant for the case that both,
python 2 and python 3, are installed simultaneously and you want
to prefer one over the other. If neither of these files work, you
may have to create a custom Makefile.lammps file suitable for
the version of Python on your system.  To illustrate, these are
example settings from the Makefile.lammps.python2.7 file:

python_SYSINC = -I/usr/local/include/python2.7
python_SYSLIB = -lpython2.7 -lnsl -ldl -lreadline -ltermcap -lpthread -lutil -lm
python_SYSPATH =
PYTHON=python2.7

python_SYSINC refers to the directory where Python's Python.h file is
found.  LAMMPS includes this file.

python_SYSLIB refers to the libraries needed to link to from an
application (LAMMPS in this case) to "embed" Python in the
application.  The Python library itself is listed (-lpython2.7) are
are several system libraries needed by Python.

python_SYSPATH refers to the path (e.g. -L/usr/local/lib) where the
Python library can be found.  You may not need this setting if the
path is already included in your LD_LIBRARY_PATH environment variable.

PYTHON is the name of the python interpreter. It is used for
installing the LAMMPS python module with "make install-python"

-------------------------

Note that the trickiest issue to figure out for inclusion in
Makefile.lammps is what system libraries are needed by your Python to
run in embedded mode on your machine.

Here is what this Python doc page says about it:

https://docs.python.org/2/extending/embedding.html#compiling-and-linking-under-unix-like-systems

"It is not necessarily trivial to find the right flags to pass to your
compiler (and linker) in order to embed the Python interpreter into
your application, particularly because Python needs to load library
modules implemented as C dynamic extensions (.so files) linked against
it.

To find out the required compiler and linker flags, you can execute
the pythonX.Y-config script which is generated as part of the
installation process (a python-config script may also be available)."

It then gives examples of how to use the pythonX.Y-config script
and further instructions for what to do if that doesn't work.