When a new theory is introduced and predicts phenomena that the previous theory couldn't should the previous theory be abandoned?
For example, Einstein's Special Relativity. We still use Newtonian mechanics while we know that the theory is wrong. It may be correct in the limit of low speeds but this doesn't mean that the theory is correct as a whole. We have evidence that disprove the theory. I understand that Newtonian mechanics are easier for calculations in everyday applications. That is, they gave the same result but they’re based on different theories.
In other words, Newton's theory provides a different explanation for the same phenomenon than Einstein's theory. Consider a scenario where two theories A and B compete about the nature of matter. Their assumptions are different. For example, in theory A atoms are assumed to be "small spheres" whereas in theory B atoms are assumed to be "small cubes". Theory B hasn't been disproved but is harder to do calculations with, while theory A has disproved but it is easier to do calculations with. In a certain range of experiments (as in low limit speed in Newtonian mechanics), they both agree.
In that range, if we use theory A isn't like we lie to ourselves if theory B is the best model we have for reality?