For　identity-based　encryption　(IBE)　with　identity　revocation,　or　simply　revocable　IBE　(R-IBE),　an　indirect　revocation　method　in　which　a　trusted　center　(i.e.,　private　key　generator,　PKG)　initially　generates　all　users’　long-term　private　keys　and　periodically　issues　time　update　keys　for　non-revoked　users　seems　to　be　a　flexible　choice,　because　it　invites　a　sender　to　generate　ciphertexts　without　caring　about　revoked　(and　non-revocked)　users.　However,　these　computation　and　communication　overheads　in　frequent　time　keys　update　operations　remain　as　a　daunting　task　for　PKG.　In　order　to　alleviate　the　offload　of　PKG　and　improve　its　scalability　in　the　quantum　computers　attack　environment,　Dong　et　al.　recently　extended　the　concept　of　R-IBE　to　support　outsourcing　computation　with　a　semi-trusted　key　update　cloud　service　provider　(KU-CSP),　and　proposed　an　outsourced　revocable　lattice-based　IBE　(OR-IBE)　scheme.　In　this　work,　we　show　that　the　OR-IBE　scheme　of　Dong　et　al.　does　not　satisfy　the　correctness　property　of　OR-IBE,　meanwhile,　it　is　not　decryption　key　exposure　resistance　(DKER),　a　default　security　requirement　for　R-IBE.　In　addition,　we　provide　a　modification　of　their　construction　to　be　a　correct　and　secure　OR-IBE　scheme.　In　particular,　the　first　lattice-based　OR-IBE　scheme　with　DKER　is　introduced.　©　2021,　Springer　Nature　Switzerland　AG.