Answer:
The fact that we observe in case of refraction through prism is, the ray gets bent or deviated towards the base of the prism. So in case of a convex lens you can imagine many prisms have been packed one above the other in the upper half portion and they are packed in the inverted position in the lower half. So as parallel beam of light rays enter through these prisms all get deviated towards the base and hence the rays get converged on the other side. Thus theonly ability of a convex lens is just to converge.
1) already converging rays after passing through a convex lens get more converged
2) parallel rays falling come out converged
3) already diverging one will go less diverged.
4) So there is chance for diverging rays after refraction through lens come out parallel.