Neural lossless image compression methods have recently achieved impressive compression ratios by fitting neural networks to represent data distributions of large datasets. However, these methods often require complex networks to capture intricate data distributions effectively, resulting in high decoding complexity. In this paper, we present a novel approach named Fitted Neural Lossless Image Compression (FNLIC) that enhances efficiency through a two-phase fitting process. For each image, a latent variable model is overfitted to optimize the representation of the individual image's probability distribution, which is inherently simpler than the distribution of an entire dataset and requires less complex neural networks. Additionally, we pre-fit a lightweight autoregressive model on a comprehensive dataset to learn a beneficial prior for overfitted models. To improve coordination between the pre-fitting and overfitting phases, we introduce independent fitting for the pre-fitter and the adaptive prior transformation for the overfitted model. Extensive experimental results on high-resolution datasets show that FNLIC achieves competitive compression ratios compared to both traditional and neural lossless image compression methods, with decoding complexity significantly lower than other neural methods of similar performance. The code will be made publicly available upon publication.