Dear Rabbi Kornfeld,
When in the course of the day, relative to the avodos in the Bais Hamikdash, did the taking of the Lulav and Arava take place?
According to RASHI (54a, DH Taka), the Aravah was stood up on the Mizbe'ach at the time that the Nisuch ha'Mayim was brought to the Mizbe'ach, which was done at the time of the morning Korban Tamid. The Lulav was taken right after that, as RASHI says on 43b (DH Lo b'Lulav).
(The above is true according to the opinion in the Gemara that says that they walked around the Mizbe'ach with the Lulav. According to the opinion that they walked around with the Aravah, then they did it right before they stood up the Aravos on the Mizbe'ach, as Rashi says there.)