Do gravitational lenses have a focus point?

It's pretty easy to see that the gravitational lens doesn't have a focal point. Please excuse my very poor drawing:

Rays from the top are focused across a line. A black hole would have a "focus line" but not a focus point.

No.

Ordinary optical lenses deflect the light ray, at least in a linear polarization, by an angle that is linear as a function of the location $(x,y)$ on the lens: $$\theta \sim ax + by$$ Well, we should really talk about $\vec k$, the wave vector, a two-dimensional angle of a sort.

On the other hand, the deflection by the gravitational lens goes like an inverse power law $$ |\theta| \sim \frac{1}{r^n} $$ for some positive $n$, just like a gravitational force. The convergence requires the linear dependence from the first formula; the second formula doesn't imitate it in any approximation.

The gravitation lens generates smaller angular deflections at large impact factors. A converging lens generates larger angular deflections at larger impact parameters.

So, a first guess would be "no way".