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Gravitational lensing is caused by the chance alignment of the observer, the lens, and the source. Obviously these are not permanent events as the earth will move in and out of a focal point as the three objects move relative to each other.

My question is: over what sort of time scales does this typically occur?

As far as I understand the focal point is quite sensitive and requires a high degree of accuracy in the alignment. Is this alignment therefore typically seen over cosmic scales of thousands or millions of years, or perhaps less? Can a gravitational lens come into and out of focus over a human life time (I imagine the source and the lens would have to be in our galaxy and probably relatively nearby for this)?

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In general no. Typical gravitational lenses are clusters of galaxies. Distant clusters move at high speeds because of the expansion of the universe. But their peculiar velocities (deviation from a pure Hubble flow) are typically hundred of km/sec, perhaps $10^{-3}$ c. In $100$ years, they might move $0.1$ light year.

Using our galaxy as an example, the thickness is around $1000$ light years and the diameter is about $100$ k light years. So the alignment of a galaxy might change by 1 part in a million over a lifetime. The alignment change of a cluster would be even less.


That said, there is one interesting gravitational lens that could change very significantly in our lifetimes. See The Solar Gravitational Lens will Map Exoplanets. Seriously.

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