Oracle program "lsnrctl" is missing after the installation of 32bit Oracle client
There doesn't appear to be a problem.

The listener is a process that generally runs on the database server, not on the client machine.  Doing a client-only install will not install a listener.  If you want to have a listener on your machine, you'd need to do a database install (though you can do a software-only install rather than actually creating a database).  

If you're just trying to connect to a remote database, however, you'd use the listener that is (presumably) running on the database server.  It's theoretically possible to install a listener on one machine for a database running on another machine but that isn't particularly common.  It would be extremely, extremely unusual to install a listener on the client machine that listens for connections to a database on a remote server.