In this work, we construct a lattice-based efficient Sequential Aggregate Signature (SAS) scheme that is provably secure in standard ideal cipher model with some slight changes. This framework is inspired by the scheme of Gentry et al. at PKC 2018 which presented trapdoor-permutation-based sequential aggregate signatures. Since to present, there is no known method to construct a lattice-based trapdoor permutation, we use lattice-based trapdoor function instead to design SAS scheme. In particular, our scheme is history-free, where the sequentially-executed aggregation operation does not need to take the previous messages in order as one part of its input. We also give software implementation of our SAS scheme using FALCON based trapdoor function, which originates from the provably secure NTRUSign signature scheme proposed by Stehle and Steinfeld at Eurocrypt 2011. The experiment results show our scheme is efficient and practical.