A lattice structure is a porous periodic structure with unit cells organized according to a pattern. Lattice structures are lightweight parts that are commonly produced by additive manufacturing techniques. Lattice structures require their topology defined, which effectively defines the connectivity of their unit cell. Many of these topologies are beam based, i.e., their unit cell is represented by a network of nodes connected with beams. Such lattice structures require a geometric modeling tool capable of generating their solid model. This article presents a method to support the topology transition for beam-based lattice structures by controlling the geometric parameters of topologies. This control is made possible with the function representation of the geometry. This work also analyzes how suitable different beam-based lattice topologies are to support the transition. A few case studies are carried out to demonstrate the feasibility of the proposed method.