When the brocha is made on the lulav we do not add on the tefillah asking for the Bais Hamikdash to be rebuilt. We do say a yehi ratzon with this request when we do Sefiras Ha’Omer. Shaking the lulav for seven days is a reminder of the Bais Hamikdash as the mishna teaches us that Bnei Yisroel would only shake the lulav on the first day. During the times of the Bais Hamikdash, those who were in the Bais Hamikdash itself shook for seven days; however, once the Bais Hamikdash was destroyed Reb Yochanan ben Zakkai established that we shake the lulav for seven days everywhere as a zecher for the Bais Hamikdash. Why don’t we ask for the rebuilding of the Bais Hamikdash when we make the brocha on lulav as we do when we count the Omer?

One answer could be that the Omer was brought on the mizbeach and therefore it is proper that when we count the Omer, we mention the yehi ratzon that we are hoping for the rebuilding of the Bais Hamikdash and when it’s rebuilt we will be able to give the mizbeach its portion. On the other hand, there was no portion of the lulav put on the mizbeach. We therefore do not say the yehi ratzon

Another response to this question is that since the lulav is shaken everywhere min ha’Torah on the first day it is not a zecher for the Bais Hamikdash. The shaking of the lulav on the subsequent days of Succos is a zecher. Since we do not say the yehi ratzon on the first day of Succos, we do not say it on the rest of the days. 

A third answer is that we say the yehi ratzon only when we do a “hazkara” (a remembering) by saying something; however, the mitzvah of lulav is an “asiyah” (activity). Therefore, Chazal did not establish to say the yehi ratzon when doing the mitzvah of lulav

Rav Shlomo Zalman Auerbach used to tell his family when they shook the lulav from the second day of Succos and on, that they should have in mind that the shaking is zecher L’Mikdash, since the takana was established for the mikdashK’lal Yisroel has a mitzvah of searching and yearning for Tzion. This would be an opportune time to think and reflect on what we are lacking.  

In this zechus we will be zocheh to shake the lulav in the rebuilt Bais Hamikdash. Amen.