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Thanks for checking other species - I had indeed forgotten that you were in Israel and I was thinking European. I'm afraid I don't know L thatuna at all, and my experience of trying to separate Lucilia by comparison of the antennae is that it is a pretty hopeless task - certainly in photos. We can discount it though, because it is a rather rare North American species, and Whitworth also notes that it tends to have a blueish sheen rather than the coppery look of cuprina and sericata.

Your specimen is old and very faded. Metallic green flies tend to go coppery with age, and you can see that the edge of her wings are raggedy.

I would expect both sericata and cuprina to be common for you in Israel, but sericata is much more likely than cuprina in an urban environment.