[Danieru]

No, because the light requires twice the time to travel there then back. If Earth did not move relative to the lens, it would work. Sadly we move, a lot, so what was here 2x ago was something not-earth.

To see earth, the lensing would been to be focused on where Earth was 2x ago. Still possible in theory, and you might even argue just as likely as a fully reflecting curve. But you'd not call it "back towards us". It would need to be "curved to where earth was".

[0xDEAFBEAD]

Seems like if you could retrodict the position of past lenses, and predict their effects, perhaps it would somehow be possible to send a spacecraft to a specific location in order to observe Earth's past.

The idea being that a spacecraft traveling at 99% of light speed can't ordinarily catch up with light reflected by Earth. But if the light curves, and the spacecraft can travel directly towards where the light will end up (spacecraft traveling "as the crow flies"), it might be possible to catch up.

Same way I might be able to catch up with Usain Bolt at a track event if he's forced to run on the track, and I'm allowed to run across the turf in the middle.

[w0de0]

https://en.wikipedia.org/wiki/Closed_timelike_curve

[deskamess]

Would this be the case even if you were moving toward or along-side the 'reflector' (black hole/other body)? For the sake of discussion assume we are at or beyond the focal point.