How does a predictive coding aid in lossless compression?
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(\cdot)$ is the (log 2) entropy function.

In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,\ldots,255,0,1,2,\ldots,255,\ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(\log n)$ bits for the entire sequence.