This paper shows how fused decomposition modeling (FDM), as a three-dimensional (3D) printing technology, can engineer lightweight porous foams with controllable density. The tactic is based on the 3D printing of Poly Lactic Acid filaments with a chemical blowing agent, as well as experiments to explore how FDM parameters can control material density. Foam porosity is investigated in terms of fabrication parameters such as printing temperature and flow rate, which affect the size of bubbles produced during the layer-by-layer fabrication process. It is experimentally shown that printing temperature and flow rate have significant effects on the bubbles’ size, micro-scale material connections, stiffness and strength. An analytical equation is introduced to accurately simulate the experimental results on flow rate, density, and mechanical properties in terms of printing temperature. Due to the absence of a similar concept, mathematical model and results in the specialized literature, this paper is likely to advance the state-of-the-art lightweight foams with controllable porosity and density fabricated by FDM 3D printing technology.