The environment variable that overrides or extends the list of directories holding shared libraries is LD_LIBRARY_PATH. This variable is used to specify a colon-separated list of directories where the dynamic linker should look for shared libraries when loading a program1. The directories in LD_LIBRARY_PATH are searched before the default directories, such as /lib and /usr/lib, or the directories specified in/etc/ld.so.conf or the executable’s rpath1. This variable can be useful for testing or debugging purposes, or for running programs that require a specific version of a library that is not installed in the system1.
The other options are incorrect for the following reasons:
LD_LOAD_PATH. This is not a standard environment variable for shared libraries. It may be confused with LD_PRELOAD, which is a variable that allows the user to specify one or more shared libraries that should be loaded before any other library, even the C library2. This variable can be used to override or modify the behavior of certain functions or symbols in the libraries2.
LD_LIB_PATH. This is not a standard environment variable for shared libraries. It may be confused with LIBPATH, which is a variable that is used on some Unix variants, such as AIX, to specify the search path for shared libraries3. On Linux, this variable has no effect4.
LD_SHARE_PATH. This is not a standard environment variable for shared libraries. It may be confused with LD_RUN_PATH, which is a variable that allows the user to specify a list of directories that should be embedded in the executable as the rpath5. The rpath is a attribute that tells the dynamiclinker where to look for shared libraries at run time5. Unlike LD_LIBRARY_PATH, LD_RUN_PATH is only effective at link time, not at run time5.
LD_RUN_PATH. This is not an environment variable that overrides or extends the list of directories holding shared libraries, but rather one that sets the rpath of the executable at link time. See the explanation for LD_SHARE_PATH above.
References:
How to set the environmental variable LD_LIBRARY_PATH in Linux
LD_PRELOAD - The secret of code injection into a running process without ptrace
LIBPATH - Wikipedia
linux - What is the difference between LD_LIBRARY_PATH and -L at link time? - Stack Overflow
ld-linux(8) - Linux manual page