./lib/...
binds an include request in the current working directory of the script. PHP will search for the desired file there, and not somewhere else. If it does not exist, inclusion and inclusion are not performed.
lib/...
allows PHP to scan its inclusion path, for example. if you have
include_path=.:/var/lib/php:/foo/bar/baz
Then PHP will sequentially try to execute
./lib/file.php
/var/lib/php/lib/file.php
/foo/bar/baz/lib/file.php
^^^^^^^^^^^^---- include path component
^^^^^^^^^^^^--- include() argument
, . , , .