Yosef Karo

“ If it is invalid because of idolatry, because it is forbidden to eat the etrog, because it is not the right species, or because it is not the right size, it is invalid both on the first day on the subsequent days (and boils invalidate all seven days (Rabbeinu Yerucham 8:3 and Ra"n ch. "Lulav haGazul") .) Those who make two days of Yom Tov can take things invalid on he first day on the second day but should not bless on them (and if somebody else has a valid lulav and etrog, they should bless on the other one with permission (his own opinion) ) . ”

“ There is one who says that the object obtained by theft or robbery is only invalid for the thief or robber themselves, but is valid for others on days besides the first day. Rem"a: Because of this one should be careful not to have a Jew themselves trim one of the [trees of the] four species of the lulav to make a lulav, because land cannot be [acquired by a changing action after it was] stolen and the generic non-Jew steals land, thus meaning that the stolen object will end up in one's hands. ”