The influence of processing intumescent bio-based poly(lactic acid) (PLA) composites by injection and fused filament fabrication (FFF) was evaluated. A raw (ANa) and two acidic-activated (AH2 and AH5) montmorillonites were added to the intumescent formulation, composed by lignin and ammonium polyphosphate, in order to evaluate the influence of the strength and the nature (Brønsted or Lewis) of their acidic sites on the fire behavior of the composites. The thermal stability and the volatile thermal degradation products of the composites were assessed. The injected and 3D-printed composites were submitted to cone calorimeter (CC), limit oxygen index (LOI), and UL-94 flammability tests. A similar tendency was observed for the injected and 3D-printed samples. The high density of strong Lewis sites in AH2 showed to be detrimental to the fire-retarding properties. For the CC test, the addition of the intumescent composite reduced the peak of heat released (pHRR) in approximately 49% when compared to neat PLA, while the composites containing ANa and AH5 presented a reduction of at least 54%. However, the addition of AH2 caused a pHRR reduction of around 47%, close to the one of the composite without clay (49%). In the LOI tests, the composites containing ANa and AH5 achieved the best results: 39% and 35%, respectively, for the injected samples, and 35 and 38% for the 3D-printed samples. For the composite containing AH2 the LOI values were 34% and 32% for injected and 3D-printed samples, respectively. Overall, the best performance in the flammability tests was achieved by the composites containing clays with only weak and moderate strength acidic sites (ANa and AH5).