When the environment variable TCL_LIBRARY is defined, Tcl's default initialization sequence takes its value to be a file system directory in which the init.tcl file should be sought first. In a proper Tcl installation, use of this environment variable should not be needed. The main use for it is in Tcl's own build and test procedures to direct initialization of a freshly built Tcl program so that it can be tested before it is installed. Other than that, it should be considered a tool for "last-resort" workarounds of broken installations, not a tool for routine use.
If what you are trying to do is set an environment variable to point to directories containing other Tcl packages, check TCLLIBPATH.
Neither TCL_LIBRARY nor TCLLIBPATH are considered by tclkit, though.
DGP That claim surprises me. What is the evidence for it? - RS I tried, in a Cygwin bash,
$ TCLLIBPATH=/usr/local/lib tclkitsh.exe
and expected its auto_path to be extended with /usr/local/lib, but it wasn't (neither with temporarily setting TCL_LIBRARY).
See also magic names and tclvars.