Most　of　the　existing　works　for　Influence　Maximization　(IM)　are　defined　over　a　ground　set.　As　the　natural　extension　of　set　space,　in　recent　years,　some　works　have　begun　to　consider　IM　on　lattice　space.　The　lattice　boosting　problem,　however,　has　not　yet　been　considered.　In　this　paper,　we　focus　on　Lattice　k-Boosting　Problem.　Because　each　edge　has　multi-boosting　stages,　it　is　an　obstacle　to　estimate　the　value　of　boosting　influence　function　by　conventional　sampling　technique.　To　overcome　this　obstacle,　we　adopt　the　largest　boosting　probability　of　each　edge　to　generate　Potentially　Reverse　Reachable　graph　(PRR　graph)　and　propose　a　boosting　parameter　of　each　boosting　edge　to　amend　it.　Additionally,　it　is　an　unbiased　estimation　of　boosting　influence.　Because　Lattice　k-Boosting　Problem　is　not　diminishing　returns　submodular　(DR-submodular),　we　simplify　Sandwich　Approach　to　Semi　Sandwich　Approach　by　finding　a　tight　DR-submodular　lower　bound,　which　also　keeps　a　data-driven　approximation　ratio.　Besides,　we　design　a　heuristic　algorithm,　namely　Ktop　Algorithm,　to　return　a　feasible　solution　of　the　original　problem.　Numerical　experiments　show　that.,　under　the　same　constraint,　selecting　each　node　with　the　stronger　boosting　power　rather　than　many　nodes　may　have　large　boasting　influences.