On the first day of sukkos there is a din of "lachem" by the arba minim that they must belong to you in order to fulfill the mitzvah. After someone has already made a bracha on his arba minim and fulfilled the mitzvah when the person then takes the arba minim again to shake them by Hallel must they also still "belong" to him with all of the dininm of "lachem". Or may he use someone else's (without making some sort of kinyan (acquisition) on them.)
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In Nitei Gavriel Hilchos Arbas HaMinim Perek 44 Sif 3 (with note 3) he brings down there that during Hallel and Hoshanos one is yotzee if they use a borrowed lulav (or similar -- i.e. the dinim of "lechem" do not apply.) In the footnote there he brings this from the Mikorei Kodoesh (Page 78) that since the ninuim of Hallel even on the first day are only m'drabbanan (the person was yotzee the mitzvah of netilas lulav d'oraisa when he took the arba minim with a bracha before Hallel) therefore one doesn't to be makpid on dinim of "lechem" (as well as chasar) since it's like the other days of sukkos that the mitzvah of netilas lulav is only m'drabbanan and doesn't require all the same dinim of the first that is m'doraisa.