On the first Yom Tov of Sukkot, one must use a lulav that belongs to him, as it is written, “On the first day you shall take (u-lekaḥtem lakhem)” (Vayikra 23:40), which literally reads as “you shall take unto yourselves,” and which the Sages interpreted to mean “of your own (mi-shelakhem),” i.e., the lulav must belong to the person performing the mitzva. Therefore, one cannot fulfill his obligation with a borrowed lulav on the first Yom Tov. During the rest of the festival, there is no requirement that the lulav belong to the person performing the mitzva, and one may fulfill the mitzva with a borrowed lulav.
If, however, a lulav’s owner gives his lulav to someone as a gift, the recipient can fulfill the mitzva with it even on the first Yom Tov. In order to avoid the possible complication of the recipient refusing to return the lulav, the owner should give the lulav to the recipient on condition that the recipient returns the lulav to him (matana al menat le-haḥzir); if the recipient does not return it within a reasonable amount of time, the condition has not been fulfilled, and the gift is annulled (Sukka 41b; SA 658:3-4).
According to halakha, a minor (a child under the age of bar or bat mitzva) can accept a gift but cannot give one. Therefore, if an adult gives a minor a lulav as a gift, the minor is unable to return it. Thus, on the first Yom Tov, one must make sure to give a minor the lulav only after all the adults have already fulfilled the mitzva (SA 658:6; see below, 5:6 n. 5).
If one of the four species is stolen, no matter how beautiful, it is invalid for performing the mitzva throughout Sukkot, as it is a “a mitzva that comes through sin” (mitzva ha-ba’a ba-aveira). However, if the owner of the stolen lulav has despaired of getting it back, and the thief gave or sold it to a third party, one may use it to perform the mitzva, since it is no longer in the thief’s possession. Nevertheless, it is forbidden to recite a berakha on this lulav, even if it was passed on to someone else, who passes it along to someone else, and so on; as long as the lulav is known to be stolen, one may not recite a berakha on it, and one who does is considered to be cursing instead of blessing (BK 94a; SA 649:1; MB ad loc. 6).
If someone who does not have a lulav arrives at the synagogue and sees a lulav there, he should ask the lulav’s owner for permission to use his lulav to perform the mitzva. If the owner is nowhere to be found and there is no way to ask his permission, the person may use the lulav without permission. It has the status of a borrowed lulav and thus cannot be used to fulfill the mitzva on the first Yom Tov, but it can be used during the rest of the festival. Normally, someone who takes an item without permission is considered a thief. However, in this case, as the person is taking something to use for a mitzva, the Sages presume that people want their belongings to be used for mitzvot. This is on condition that the borrower does not take the lulav from its place and is very careful with it (Rema 649:5). If the lulav owner is known to be especially particular about his belongings, then it is forbidden to use his lulav without his permission, even to perform the mitzva (MB ad loc. 34).