I think this already exists in tcp_slowtmr.

    /* Check if this PCB has stayed too long in FIN-WAIT-2 */
    if (pcb->state == FIN_WAIT_2) {
      /* If this PCB is in FIN_WAIT_2 because of SHUT_WR don't let it time out. */
      if (pcb->flags & TF_RXCLOSED) {
        /* PCB was fully closed (either through close() or SHUT_RDWR):
           normal FIN-WAIT timeout handling. */
        if ((u32_t)(tcp_ticks - pcb->tmr) >
            TCP_FIN_WAIT_TIMEOUT / TCP_SLOW_INTERVAL) {
          ++pcb_remove;
          LWIP_DEBUGF(TCP_DEBUG, ("tcp_slowtmr: removing pcb stuck in FIN-WAIT-2\n"));
        }
      }
    }

The mailing list discussion with more information starts here:

https://lists.nongnu.org/archive/html/lwip-users/2018-06/msg00015.html

I just wanted to clarify the comment above about half-closed connections: Say a raw lwIP client connects with tcp_connect() and then shutdowns the Tx side of the connection, because the client expects data to automatically flow upon connection only from the server to the client. lwIP should consider this half-closed connection to be a normal connection that is still working fine.