18 USC 44 § 922(a)(5)(B)
"It shall be unlawful [...] for any person [...] to transfer, sell, trade, give, transport, or deliver any firearm to any person [...] who the transferor knows or has reasonable cause to believe does not reside in [...] the State in which the transferor resides; except that this paragraph shall not apply to [...] the loan or rental of a firearm to any person for temporary use for lawful sporting purposes"
Note, however, that you must receive the loaned firearm within your state of residence if you want to have possession of it there, or you will be violation of § 922(a)(3), which does not allow you to bring firearms into your home state that you acquired out of state (except long guns from a dealer).