This paper presents a novel High Efficiency Video Coding (HEVC) based screen content coding scheme providing lossy-to-lossless compression support. The paper follows a two-layer design approach which allows for backward compatibility with the conventional HEVC standard for the base-layer and yields lossless compression when decoding the enhancement-layer. The system employs Golomb based binarization and context-based arithmetic coding to efficiently encode the enhancement-layer. Performance evaluations using 4:4:4 screen content sequences are carried out. The results show that the proposed system substantially outperforms lossless intra- HEVC and single-layer JPEG-LS.