In　this　paper,　we　consider　a　streaming　model　of　maximizing　monotone　lattice　submodular　function　with　a　cardinality　constraint　on　the　integer　lattice.　As　(lattice)　submodularity　does　not　imply　the　diminishing　return　property　on　the　integer　lattice,　we　introduce　the　Sieve-Streaming　algorithm　combining　with　a　modified　binary　search　subroutine　to　solve　the　problem.　We　also　show　it　is　with　an　approximation　ratio　1　/　2　-　,　a　memory　complexity　O(-　1klog　k),　and　a　query　complexity　O(-　2log2k)　per　element.　©　2021,　Springer　Nature　Switzerland　AG.