or visa-versa, rays coming out from a point into a parallel beam.

If you work it out precisely this is actually an approximation.

The approximation is un-noticeable for most practical purposes

but can become important for very strong (very fat) lenses.

Your problem is that you have light rays diverging from several points

which you want to focus through a single point

and then on (through more lenses) to produce a parallel beam.

A standard point focus lens is based on sections of spheres

A line focus lens can be constructed from sections of cylinders.