The soft context formation coder is a pixel-wise state-of-the-art lossless screen content coder using pattern matching and color palette coding in combination with arithmetic coding. It achieves excellent compression performance on screen content images in RGB 4:4:4 format with few distinct colors. In contrast to many other lossless compression methods, it codes entire color pixels at once, i.e., all color components of one pixel are coded together. Consequently, it does not natively support image formats with downsampled chroma, such as YCbCr 4:2:0, which is an often used chroma format in video compression. In this paper, we extend the soft context formation coding capabilities to 4:2:0 image compression, by successively coding Y and CbCr planes based on an analysis of normalized mutual information between image planes. Additionally, we propose an enhancement to the chroma prediction based on the luminance plane. Furthermore, we propose to transmit side-information about occurring luma-chroma combinations to improve chroma probability distribution modelling. Averaged over a large screen content image dataset, our proposed method outperforms HEVC-SCC, with HEVC-SCC needing 5.66% more bitrate compared to our method.