Maximization　of　non-negative　monotone　submodular　set　functions　under　a　knapsack　constraint　have　been　extensively　studied　in　the　last　decade.　Here,　we　consider　the　streaming　algorithms　of　this　problem　on　the　integer　lattice,　or　on　a　multi-set　equivalently.　This　is　more　realistic　for　many　practical　problems　such　as　sensor　location　and　influence　maximization.　It　is　well　known　that　submodularity　and　diminishing　return　submodularity　are　not　equivalent　on　the　integer　lattice.　We　mainly　focus　on　maximizing　the　diminishing　return　submodular　(DR-submodular)　functions　with　knapsack　constraint　on　the　integer　lattice.　Finally,　by　utilizing　the　binary　search　algorithm　as　a　subroutine,　we　design　an　online　streaming　algorithm　called　DynamicMRT.　Furthermore,　we　prove　that　it　is　a　(1　/　3　-　Ε)　-approximation　algorithm　with　O(Klog　K)　memory　complexity　and　O(log　K)　query　complexity　per　element.　©　2021,　Springer　Nature　Singapore　Pte　Ltd.