A handcuff graph is a graph consisting of disjoint two loops and connected by an edge. The lattice stick number of a handcuff graph is the minimum number of sticks required to embed the graph in a lattice space. Previous studies have shown that the lattice stick numbers of the trivial handcuff graph and the Hopf-linked handcuff graph are 9 and 11, respectively, and these are the only graphs whose lattice stick number is 13 or less. In this talk, we utilize a squeezing method to identify all models with a lattice stick number of at most 14.