In　the　article,　we　devise　streaming　algorithms　for　maximization　of　a　monotone　submodular　function　subject　to　a　cardinality　constraint　on　the　integer　lattice.　Based　on　the　observation　that　lattice　submodularity　is　not　equivalent　to　diminishing　return　submodularity　on　the　integer　lattice　but　rather　a　weaker　condition,　we　propose　a　one-pass　streaming　algorithm　with　a　modified　binary　search　as　subroutine　of　each　step.　Finally,　we　show　that　the　algorithm　is　with　approximation　ratio　(Figure　presented.),　memory　complexity　(Figure　presented.),　and　per-element　query　complexity　(Figure　presented.).　©　2021　John　Wiley　&　Sons　Ltd.