For　group　signatures　with　verifier-local　revocation　(GS-　VLR　),　selfless-anonymity　(SA),　which　only　ensures　the　anonymity　of　a　signature　against　an　adversary　not　possessing　the　signing　secret-keys　for　members　who　were　involved　in　the　generation　of　the　challenge　signature,　is　strictly　weaker　than　the　de　facto　standard　anonymity　notion,　full-anonymity,　where　the　adversary　is　allowed　to　corrupt　all　members.　At　ICICS　2018,　Hou　et　al.　delivered　a　lattice-based　fully　anonymous　GS-　VLR　scheme　(as　one　core　building　block　for　their　semi-generic　construction　of　hierarchical　GS-　VLR　)　based　on　the　first　lattice-based　GS　scheme　introduced　by　Gordon　et　al.　at　ASIACRYPT　2010.　In　this　paper,　we　demonstrate　that　their　scheme　does　not　consider　the　anonymity　for　revoked　members　(no　matter　the　misbehaving　members　or　the　honest　ones　who　voluntarily　leave),　an　implicit　requirement　for　GS-　VLR　in　a　real-life　application.　Subsequently,　we　provide　a　modification　of　their　construction　to　fix　the　mentioned　weakness.　©　2021,　Springer　Nature　Switzerland　AG.