OWL_DISABLE_LAPACKE_LINKING_FLAG=1 disables the -llapacke flag in the linking options. This is useful when you have lapacke installed on non-standard localtion.
If you are not using opam, you should run make clean before recompiling the library after having changed any of those environment variables.
For examples of use of this feature, you can refer to the Docker.ubuntu and Docker.ubuntu.arm docker files, or to the snippet in https://github.com/owlbarn/owl/issues/394#issuecomment-471364916 (which also shows how to use it within esy).
Troubleshooting
A common source of frustration when installing owl is the possible appearence of linking errors (see for example https://github.com/owlbarn/owl/issues/450). This usually happens when installing owl on ubuntu (where it depends on how openblas is complied and packaged), but could happen in other distributions (see for example https://discuss.ocaml.org/t/owl-undefined-symbols-after-standard-installation/4186/13). The only way we could solve those issues is to recompile openblas and install it manually. You can see how we do it by looking at the Docker files in the repository: https://github.com/owlbarn/owl/blob/master/docker/Dockerfile.ubuntu