Boyen and Li [AsiaCrypt, 2016] proposed the first almost tightly secure lattice identity-based encryption scheme in the standard model. The security of such scheme is proved under learning with errors assumption in the single-instance, single-challenge setting. In this work, we show how to extend the Boyen-Li scheme to obtain an almost tight security reduction in the multi-instance, multi-ciphertext setting, in which the security loss incurred is poly(κ) in the security parameter κ and independent of the number of adversarial queries.