This paper considers the problem of universal lossless source coding with side information at the decoder only. The correlation channel between the source and the side information is unknown and belongs to a class parametrized by some unknown parameter vector. A complete coding scheme is proposed that works well for any distribution in the class. At the encoder, the proposed scheme encompasses the determination of the coding rate and the design of the encoding process. Both contributions result from the information theoretical compression bounds of universal lossless source coding with side information. Then a novel decoder is proposed that takes into account the available information regarding the class. The proposed scheme avoids the use of a feedback channel or the transmission of a learning sequence, which both would result in a rate increase at nite length. Simulations are based on irregular and non-binary LDPC codes and show that, even at nite length, the proposed scheme performs close to the theoretical bound.