It looks like something is wrong with your installation, i.e. the DBD::Oracle module is installed in a system directory but not its libclntsh.so.11.1 dependency. That's something for the sysadmin to fix---link the library to a dir in the standard library path, extend the path in /etc/profile or something.

As a workaround, you can specify a full shell command line including variable setting in a crontab as well. Or do something evil like (untested, prone to DOSing the system if something goes wrong, and hopefully unnecessary anyway)

eval "use DBD::Oracle;";
if($@) {
   $ENV{LD_LIBRARY_PATH} = '/where/ever/the/hell';
   exec $0 @ARGV;
}
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