use lib "/users/<myusername>/perl/Tk-DKW-0.03/blib";
is correct. Perl wants to load Tk/Menustrip.pm, so the directory name must end in blib, not blib/Tk.
Better solution: don't edit the example and simply set the include path from the commandline:
$ cd /users/<myusername>/perl/Tk-DKW-0.03
$ perl -Mblib examples/checkbox.pl
Update: this half-installed directory setup is only useful for testing. If you want to use Tk-DKW productively, you must install the distribution. local::lib helps you to set up the necessary environment variables so that the make install will target your home directory, not the system location where you have no write permission.