Both populations of lizards would begin to accumulate different mutations
And to add to this, mutations would not even be necessary in your excellent scenario. Directional selection and Genetic drift could simply take place to such a degree, a group speciates.
Directional selection would be moving in a certain direction as the environment demands. So, if a long tail is advantageous, then the lizards with the longest tails would be reproductively more successful, and in time, the entire population has longer tails than the other side of the river. Add to that genetic drift, which is what happens when genes are limited to a smaller pool, and over time, the gentic makeup of the long tailed lizards become very different from the other side of the river. Since the two populations are separate from each other, there is no gene flow--in other words a sharing of genes, and eventually the two would no longer be genetically capable of reproducing. Add to that sexual recognition, and it gets even more interesting. The short tailed lizards recognize other short tailed lizards as mates. If they were to bump into a long tailed lizard, in spite of them having come from a common population, they would not even recognize them as mates.