The last few years witnessed an increased interest in the robust lossless data hiding schemes because they can verify the main requirements of the lossless data hiding (i.e., reversibility, capacity, and invisibility) and at the same time provide robustness against attacks. The reversibility is one of the important requirements of those methods. Another important requirement is the improvement of the robustness against attacks. The methods that improve the robustness are at the cost of reducing capacity and invisibility. Taking into consideration the need for improving the four requirements that have been mentioned above, this paper presents a novel robust lossless data hiding method in the transform domain. The proposed algorithm depends on transforming non-overlapping blocks of the host image using Slantlet transform (SLT) matrix and embedding data bits by modifying the difference between the mean values of the SLT coefficients in the high frequency subbands. As a practical application, the proposed algorithm has been adjusted in order to be applied to the color medical images. The data bits can be embedded not only in a single channel but also in the three channels of the RGB color image and thus further improving the embedding capacity. The results of the experiments that were conducted and the comparisons with the previous robust lossless data hiding (i.e., robust reversible watermarking) methods prove the effectiveness of the proposed algorithm.