LOR implies unpredictability?
The reduction will not work. The reason is that any $E$ that is LoR indistinguishable has to be randomized. But then, the adversary's output might be different from the outcome of the oracle, even if it evaluates the correct $x$ (the one picked by the adversary).

In fact, there is a family of $E$'s that is predictable but still LoR indistinguishable. For example consider a public-key encryption scheme that is LoR indistinguishable and let $E(x)=(\mathit{Enc}(\mathit{pk},x),\mathit{pk})$. Then also $E$ is LoR indistinguishable. However, you can easily find pairs $(x,E(x))$ since with one query you can retrieve the public key.