Two galaxies aligned in a way where their gravity acts as a compound lens

Even assuming a civilization can predict the alignment of the lenses (galaxies), they'd still need quite a powerful signal just to reach the first lens, let alone the second, and then a potential civilization who may be listening at just the right time on the other side. Hard to beat background noise even at distances of a few light years.

But if you can do that, you know you have plenty of time for a civilization to develop on the other end to listen.

Might just not be us.

That's assuming the development of the two civilizations starts simultaneously and is predictable to the point the signal reaches the other side. That side of the lenses may never see a civilization developing at all, or at least not one surviving long enough to receive that obscure signal.

These distances and time periods are unfathomably long. I can see predicting the alignment of galaxies but predicting a civilization with an adequate evolution stage will exist at the right spot, at the right time is very different. Any civilization with this power of prediction probably has a level of advancement that makes the difference between humans and amoeba look positively non-existent, and probably wouldn't bother with broadcasting lowly radio waves into the universe.

I can't imagine the universe and evolution of life being so deterministic and predictable especially over this time scale, no matter what tech you have.

Over such timescales since you'd aim at another galaxy wholesale you coud bet on Drake equation plus hope a civilisation has survived long enough for a wide enough window to be able to receive the transmission.

> probably wouldn't bother with broadcasting lowly radio waves into the universe.

I bet we would be very glad to receive such a transmission, even when knowing full well "replying" isn't a realistic option (both due to technology limitations and the RTT meaning that even if the reply receives were descendants, they'd be so far removed as to be entirely another ship-of-theseus civilisation)

A gift in a cosmic dying sigh could be motivation enough.

"Should anyone receive this, know that, as far as life forms go, you were not quite alone and life existed beyond yours. We're sending this knowing full well we'll be long gone, but during all of our civilisation history we could only hypothesise that we were not. We hoped but never knew, may this transmission relieve you of the doubts we had; you now unambiguously know."

At that point you might just as well send out a high power broadcast of Never Gonna Give You Up and congratulate yourself on a job well done, indulging in imaginations of fantastic ways of how it might get received somewhere half a universe lifespan later.