you could add it to your PATH

I did all this, but what has it availed me?

$ ./5.sscce.pl
bash: ./5.sscce.pl: No such file or directory
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Note that ./script.pl tells the shell to only look in the current directory. If you run a shell command without the ./ or any other path name, the shell will look in your PATH for a file by that name and run it (it needs to have executable permissions).

use lib "lib"; ... I don't completely understand how and why people use it.

Once you've added the script to your PATH and are able to call it from any directory, relative paths used to load libraries will no longer work. That's what my FindBin example does: it'll locate the directory where the script is, no matter what the current working directory is, and then use the lib directory relative to the script's location, not the current working directory.