Group signatures are an important anonymity primitive allowing users to sign messages while hiding in a crowd. At the same time, signers remain accountable since an authority is capable of de-anonymizing signatures via a process called opening. In many situations, this authority is granted too much power as it can identify the author of any signature. Sakai et al. proposed a flavor of the primitive, called Group Signature with Message-Dependent Opening (GS-MDO), where opening operations are only possible when a separate authority (called " admitter ") has revealed a trapdoor for the corresponding message. So far, all existing GS-MDO constructions rely on bilinear maps, partially because the message-dependent opening functionality inherently implies identity-based encryption. This paper proposes the first GS-MDO candidate based on lattice assumptions. Our construction combines the group signature of Ling, Nguyen and Wang (PKC'15) with two layers of identity-based encryption. These components are tied together using suitable zero-knowledge argument systems.