There's a lot of questions and issues you face at the same time. I'd suggest breaking this down and making sure the foundation works first.
LwIP is a TCP/IP stack so you don't need another one. You first need to get LwIP running, and about the simplest parts here is making sure it responds to ping messages.
When you have ping running reliably, make sure you can get one of the simple apps provided with LwIP - iperf or httpd - running.
You should now have a good enough foundation to start using OpENer.