In the BLFS book, just for comparison, the expect page lists the shared library being installed just as you discovered in your LFS tools dir (not a static library as the LFS book says). The configure command in the BLFS book includes --enable-shared which would install the .so library. Even though the LFS expect page does not include the --enable-share configure option, the configure --help information for expect-5.45 (which I just looked at) states that --enable-shared is the default. So I would expect the installed library to be the .so as you found. This exact situation seems to go back to at least LFS v6.8 which used the same version of expect. To me, this is probably a simple typo in the LFS book. If you like, you can report it either by creating a new ticket at the LFS wiki or by posting it in one of the LFS mailing lists (say, lfs-dev or lfs-support). I've reported stuff like that both ways. Doesn't really matter much since the same guys all read all of that stuff. They seem to appreciate it. Go to
http://www.linuxfromscratch.org/ and follow links to the wiki or the mailing lists.