Yosef Karo

“ The whole day is fitting for taking the lulav; if one did not take it in the morning, they can take it later. In any event, those who are prompt do mitzvahs early and take it in the morning. Its time starts at sunrise. The core time to do the mitzvah is during Hallel. If somebody needs to wake up early to travel, they should take it at dawn. Rem"a: One who is precise should hold the lulav in their hand when entering the house or the synagogue, even during prayers, and also when returning home, so as to be affectionate towards the mitzvahs (Tur) . ”