I'm no mathematician but I don't believe this is true. Lossless information encoding requires all the original information to be present.
Have the de-compressor predict the next data based on the outcome so far (a statistical prediction of next data will be lossy as it won't always be correct). If the prediction is correct you need to spend very little to confirm that. If it's incorrect you'll need to spend data to correct it. Arithmetic coding is the best way to make this work.
It's also been used by all winning entries of the Hutter prize so far.