Liposomes are considered as advanced drug delivery systems for cancer treatment. A generation of pH-sensitive liposomes is being developed that use fatty acids (FAs) as a trigger for drug release in tumor tissues. However, FAs are also known to enhance permeability, and it is unclear whether FAs in liposomes may cause drug leakage or premature drug release. The passive permeability of the drug through the membrane of the liposome is thus a crucial factor for timely drug delivery. To investigate how the curvature and lipid composition of liposomes affect their passive permeability, coarse-grained molecular dynamics were performed. The permeability was determined with a counting method. Flat bilayers and three liposomes with varying diameters were studied, which had varying lipid compositions of dipalmitoylphosphatidylcholine, cholesterol, and deprotonated or neutral saturated FAs. The investigated permeants were water and two other small permeants, which have different free energy profiles (solubility) across the membrane. First, for the curvature effect, our results showed that curvature increases the water permeability by reducing the membrane thickness. The permeability increase for water is about a factor of 1.7 for the most curved membranes. However, a high curvature decreases permeability for permeants with free energy profiles that are a mix of wells and barriers in the headgroup region of the membrane. Importantly, the type of experimental setup is expected to play a dominant role in the permeability value, i.e., whether permeants are escaping or entering the liposomes. Second, for the composition effect, FAs decrease both the area per lipid (APL) and the membrane thickness, resulting in permeability increases of up to 55%. Cholesterol has a similar effect on the APL but has the opposite impact on membrane thickness and permeability. Therefore, FAs and cholesterol have opposing effects on permeability, with cholesterol's effect being slightly stronger in our simulated bilayers. As all permeability values were well within a factor of 2, and with liposomes usually being larger and less curved in experimental applications, it can be concluded that the passive drug release from a pH-sensitive liposome does not seem to be significantly affected by the presence of FAs.