In this paper, we explore mathematical links, defined as closed curves embedded in 3D space. Knot theory studies these structures, which also occur in real-world biopolymers like DNA. Lattice links are links in the cubic lattice. For scientific simulations or statistical studies, links are simplified to lattice links. The lattice stick number, denoted as s L (K), is the minimum number of lattice sticks needed to represent a link K in the cubic lattice. In previous study, it was shown that only two non-trivial knots and six non-splittable links have s L ≤ 14: specifically, sL(212)=8 , sL(31)=sL(212♯212) = sL(623)=sL(633)=12 , sL(412)=13 , and sL(41)=sL(512)=14 . Recent study has further revealed that no knot can have s L = 15. In this paper, we prove that lattice stick number 15 is not attainable for non-splittable links. As a corollary, eleven non-splittable links with s L =16 are presented.