Common representations of light fields use four-dimensional data structures, where a given pixel is closely related not only to its spatial neighbours within the same view, but also to its angular neighbours, co-located in adjacent views. Such structure presents increased redundancy between pixels, when compared with regular single-view images. Then, these redundancies are exploited to obtain compressed representations of the light field, using prediction algorithms specifically tailored to estimate pixel values based on both spatial and angular references. This paper proposes new encoding schemes which take advantage of the four-dimensional light field data structures to improve the coding performance of Minimum Rate Predictors. The proposed methods expand previous research on lossless coding beyond the current state-of-the-art. The experimental results, obtained using both traditional datasets and others more challenging, show bit-rate savings no smaller than 10%, when compared with existing methods for lossless light field compression.