You have to pay closer attention to the compilation instructions in the manual.
Typing make yes-openmp installs the OPENMP package code, but it does not activate compilation with OpenMP support enabled or compile LAMMPS. Your entire quoted command line only installs/uninstalls packages, but there is no mention of a compilation.
Your command for running LAMMPS only uses MPI parallelism and does not seem to enable the omp suffix. Furthermore the --bind-to core option will prohibit multiple threads to run on different CPU cores.
We generally recommend people with limited experience in customizing makefiles and compiler flags to build LAMMPS using CMake. This can and will autodetect and enable OpenMP and MPI support transparently, if your software installation supports it.
Of course, you can only have multi-threaded execution, if you are using styles for which multi-threaded versions exist.
A good test can be made using the statically linked pre-compiled executable from LAMMPS Static Linux Binary Download Repository: .
This has the OPENMP package (and most other packages) included and OpenMP enabled (but no MPI).
You can run with env OMP_NUM_THREADS=8 ./lmp -in equ.in -sf omp and the run should multi-thread across 8 CPU cores, if the input uses styles with multi-thread support.