Do all lazy eyes lead to bad vision?

Strabismus . I am assuming that what you mean is crossed or turned eyes. If so, the answer is no. Amblyopia or bad vision is more commonly associated with inward turning (crossed) eyes.
Yes... Lazy eyes are actually eyes that do not have good vision, either due to a misalignment of the eye or a block in the vision (uncorrected prescription need, cataract, scar). So poorly seeing eyes can lead to lazy eyes and vice versa.