Some chassidim have the practice of leaving shul, after shacharis, each day of Succos, in order to shake their lulav in the succah before reciting Hallel. The origin of the minhag most probably was that one who had slept in the succah all night would wash his hands first thing in the morning and recite the bracha over the lulav right after sunrise. But based on Kabalah sources there has developed a minhag that even when one has not slept in the succah, and even if it's not first thing in the morning, one should combine the two mitzvos of succah and lulav[1].
The mitzvah of succah symbolizes the survival of the Jewish people during the forty year period after leaving Egypt prior to entering Eretz Yisroel (under the leadership of Yehoshua bin Nun). By now this mitzvah has also come to represent the miraculous survival of the Jewish people through all the exiles and all the pogroms they suffered. The mere existence of our people today is really "stranger than fiction"[2] and supernatural!
On the other hand, the mitzvah of lulav represents those time periods when the Jews lived in Eretz Yisroel. The farmer would dance before Hashem thanking Him for the bounty He had blessed him with[3].
Perhaps the idea behind combining the two mitzvos of the lulav and the succah is to emphasize the idea that all of Jewish history was charted out by Hashem. There are those who feel that the many years we spent in golus were an accident of fate, and that now that we have our own Jewish medinah in Eretz Yisroel, we ought to discontinue the study of the Babylonian Talmud along with all the other seforim composed during those years of golus. They feel that we should disassociate ourselves from everything that was developed during the golus period. This is not our approach. One of the reasons given by the rabbis of the Medrash as to why Avaraham Avinu was referred to by the Torah as "Avraham Haivri", and the entire Jewish nation after him are known as "ivrim" is because he came mei'ever hanahar (from the other side of the river)[4]. The rabbis did not mean this simply as a geographic description. They meant to bring out that Avraham maintained all the principles of faith he had discovered "on the other side of the river" even after Hashem gave him Eretz Yisroel.
The Talmud (Avodah Zara 5a) records a tradition that Hashem showed Adam Harishon a book that consisted of "dor dor vachachamav -each generation and its Torah scholars". In that book there was mention of Rav, Shmuel, Ravina and Rav Ashi as leading figures in the development of the Torah Shebeal Peh in Bavel (Bava Metziah 85b - 86a). Towards the end of the tochacha in parshas Bechukosi (Vayikra 26:44) we read that even when the Jews will be in golus, Hashem will not have totally despised them or totally rejected them, because of the bris (the covenant) that He had previously made with them. The Talmud (Megillah 11a) takes that passuk as an allusion to the prominent leaders that Hashem had sent to guide us.
The two mitzvos of Succos - the succah and the lulav - represent the two parts of Jewish history; the years of golus and the years of living in Eretz Yisroel. We believe that all is from Hashem, and that all that Hashem does is always for the good[5]. Even during periods of hester ponim [6]it is not the case that Hashem was not watching over us! Hashem was hiding from us in such a way that we could not see His face (i.e. hester ponim), but all the while He was, so to speak, "peeking through the cracks" (see Shir Hashirim 2:9) and looking after us[7]. Hashem has guided, from behind the scenes, the history of the Jewish people, as well as the development of the Torah Shebeal Peh, in such a way that both reach successful conclusions.
[1] Based on Shalah, masechet Succah (p. 75d), referred to by the Magen Avraham (652, 3).
[2] Which is the title of an English book on Jewish history
[3] see Rambam in Morah Nevuchim (3, 43) and "Insights of Rabbi J.B. Soloveitchik", by Rabbi Saul Weiss, p. 103
[4] see Rav Soloveitchik's essay on Avraham Haivri, section 4, in "Five Droshos"
[5] see Berachos (60b) where the famous story about Rabbi Akiva is recorded. The rabbis felt that even something that seems to us to be absolute evil, really contains something good which we can not perceive. Some have commented on the expression used in the Torah (Devarim 25:19) in connection with the mitzvah to wipe out Amalek "from under the heavens", that the connotation is that from Hashem's perspectvive (mai'al hashomayim) there is some good in Amalek also. And indeed the rabbis of the Talmud had a tradition (Gittin57b) that many years later, descendants of Haman (the Amaleiki) converted and learned Torah in Bnei Brak. See also Sanhedrin 96b.
[6] see Devarim 30:17-18 and 32:20
[7] see Yad Haktanah pp. 39, 242