I have recently tried to compile lwip on gcc 9, clang 9 and gcc-arm 9 and have run into the same error "conflicting types for ssize_t".  In each case SSIZE_MAX was not defined so ssize_t type was declared as int, see code sample below.

Unfortunately I am not experienced enough with all the different possible platforms to know the ideal solution for this (if there is even one), but some suggestions are:

1 - Use #include <stddef.h>
2 - Allow the user to define ssize_t in lwipopts.h
3 - Use _SIZE_TYPE_ or _SSIZE_T_DECLARED instead of SSIZE_MAX (this is declared in types.h"

Another important point is that defining ssize_t as int may be incorrect as it is may need to be defined as a long int (e.g. 64 bit systems).  If it is necessary to declare it as int, use _INT_MAX_ to decide if it should be int or long int (as per _types.h shown below).  In most cases this would probably remove the compiler warning as it would be defined as the same type from types.h.  This is what I have done for now.

#if defined(_INT_MAX_) && _INT_MAX_ == 2147483647
typedef int _ssize_t;
#else
typedef long _ssize_t;
#endif

Current code from line 118 of arch.h

#ifdef SSIZE_MAX
/* If SSIZE_MAX is defined, unistd.h should provide the type as well */
#ifndef LWIP_NO_UNISTD_H
#define LWIP_NO_UNISTD_H 0
#endif
#if !LWIP_NO_UNISTD_H
#include <unistd.h>
#endif
#else /* SSIZE_MAX */
typedef long int ssize_t;
#define SSIZE_MAX INT_MAX
#endif /* SSIZE_MAX */