The Talmud identifies two types of religious objects: a 'Holiness
object', such as Tefillin, or a Sefer Torah, and a 'Mitzvah object', such
as Tzitzis. The former, due to its sanctity, must be buried in a Jewish
cemetery when it is no longer useful. A Mitzvah object, although we
respect it as well, is exalted only insofar as it is useful in the
performance of a Mitzvah. Once that usefulness is gone, its exalted status
is gone too, and we may dispose of it - not in a disrespectful way, but
not in any special way. So, for example, a worn-out pair of Tzizis may be
placed in a plastic bag by itself and disposed of in the trash.
A lulav is deemed to be a 'Mitzvah object', since its function is to
perform the mitzvah of the four species on Succot. Once the festival has
passed, there is no longer a mitzvah, and you are permitted to dispose of
it. The 'custom' of putting it on top of the Aron [Ark] in Shul actually
applies to beaten hoshanos [willow branches] on Hoshanah Rabbah, not to a
lulav. Even there, the custom itself is erroneous, since it is prohibited
to use the Aron Kodesh for anything other than storing a Sefer Torah. This
is noted by several commentators to the Shulchan Aruch [Code of Law].
Finally, there *is* a valid custom regarding the post-Sukkot lulav, and
that is to store it until the 14th of Nissan and use it as firewood to burn
the Chametz [leaven]. This follows the maxim that an object used for one
mitzvah should be used for another one as well. By that time, six months
after Sukkot, the lulav is dried out and burns rather well. Some
additionally add the used wicks from Chanukah into the Chametz fire.