Despite well-known side effects, nonsteroidal anti-inflammatory drugs (NSAIDs) are one of the most prescribed drugs worldwide for their anti-inflammatory and antipyretic properties. Here, we report the effects of two NSAIDs, aspirin and indomethacin, on the thermotropic phase behavior and the dynamics of a dioctadecyldimethylammonium bromide (DODAB) lipid bilayer as studied using neutron scattering techniques. Elastic fixed window scans showed that the addition of aspirin and indomethacin affects the phase behavior of a DODAB bilayer in both heating and cooling cycles. Upon heating, there is a change in the coagelto fluid-phase transition temperature from 327 K for pure DODAB bilayer to 321 and 323 K in the presence of aspirin and indomethacin, respectively. More strikingly, upon cooling, the addition of NSAIDs suppresses the formation of the intermediate gel phase observed in pure DODAB. The suppression of the gel phase on addition of the NSAIDs evidences the synchronous ordering of a lipid headgroup and chain. Analysis of quasi-elastic neutron scattering data showed that only localized internal motion exists in the coagel phase, whereas both internal and lateral motions exist in the fluid phase. The internal motion is described by a fractional uniaxial rotational diffusion model in the coagel phase and by a localized translation diffusion model in the fluid phase. In the coagel phase, the rotational diffusion coefficient of DODAB is found to be almost twice for the addition of the drugs, whereas the mobility fraction did not change for indomethacin but becomes twice for aspirin. In the fluid phase, the lateral motion, described well by a continuous diffusion model, is found to be slower by about, similar to 30% for indomethacin but almost no change for aspirin. For the internal motion, addition of aspirin leads to enhancement of the internal motion, whereas indomethacin did not show significant effect. This study shows that the effect of different NSAIDs on the dynamics of the lipid membrane is not the same; hence, one must consider these NSAIDs individually while studying their action mechanism on the cell membrane.