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An aggregate signature turns multi-message multi-authentication into multi-message single-authentication, reducing the required storage space, transmission cost, and number of verification calculations, and is suitable for fast message authentication in the big data era, particularly in wireless sensor networks and secure email systems. Many aggregate signature schemes have been proposed, including lattice-based ones, which have good resistance to quantum machine attacks. However, the existing lattice-based aggregate signature schemes, which either have strict requirements on the signing order or encounter security risks, are not suitable for the unordered polymerization environment. In this paper, we accordingly propose a lattice-based unordered aggregate signature scheme. The proposed scheme makes use of the intersection method and solves the unordered aggregate problem of lattice signatures with different public keys. Therefore, it avoids both the signing order limitation and the risk of single signature forgery. Furthermore, the scheme follows the improved security model; hence, it is robust against collusion attacks. In addition, the scheme's security depends on the small integer solution problem, which enables the scheme to resist quantum algorithm attacks.