Are discrete systems defined by LCCDE always LTI?
What you have is a so-called behavior which truncates the signal space $\mathcal{X}\oplus\mathcal{Y}$ of all possible signal pairs $(x, y)$ to the ones that satisfies this equality. 

This does not specify an input-output mapping and hence a dependence and hence causality does not apply here. They simultaneously satisfy this. However regardless of causality, it is LTI since you can take arbitrarily and superposition applies.

Just like you can integrate any differential equation sufficiently many times and end up with a integral equation, you can also forward time shift these equations then if one of them depends on future inputs and that is your choice of dependent variable then you can speculate about causality.

This is actually the tool to allow for nondifferentiable input signals and other discontinuities and the results are investigated under the name of weak solutions