Socket Programming without RTOS

The LWIP stack without an RTOS is not sockets API compliant; it has its own API and the receive is likely interrupt-callback-based. Having an RTOS can actually make things easier once you're familiar. I found that the Micrium textbook that discusses the MicroC/OS features to be very good.

As an alternative you could try out eCOS; there are books available on it, and I believe it includes a sockets-compliant stack. eCOS is (I believe) free; uC/OS is not (well, free for use on the nios dev boards with purchase of a nios kit), but I understand that purchasing a license for an end application gives you support from Micrium as well. Micrium also has a network stack product.