With SQLite 3.13.0 using the autoconf tarball, running ./configure without arguments does not automatically check for readline. This used to work in SQLite 3.8.4. The reason is that the default value for "enable-readline" is set to "no" in configure.ac. The fix is easy:
diff -ru a/configure.ac b/configure.ac --- a/configure.ac 2016-05-20 11:37:09.548488947 +0200 +++ b/configure.ac 2016-05-20 11:37:21.918632861 +0200 @@ -41,7 +41,7 @@ AC_ARG_ENABLE(readline, [AS_HELP_STRING( [--enable-readline], [use readline])], - [], [enable_readline=no]) + [], [enable_readline=yes]) if test x"$enable_editline" != xno ; then sLIBS=$LIBS LIBS=""