Here's what I see:
On the client side, you should not bind() the socket to an IP. You just need to use connect()
You do not want to keep connecting to find the IP of your server. You should give it a static IP address, or you can use the Pi mDNS name raspberrypi.local.
Can you clarify your setup a little? I assume that your server is the Pi because it's controlling the LEDs, but what is your client device? A computer?
Have you looked at
https://docs.python.org/2/howto/sockets.html? This doc will explain basic socket usage.