Red-banded hairstreaks really ARE as common as dirt down here, seedmoney, but I've never found an egg, caterpillar, or chrysalis. I would assume they get a lot of opportunity to go through their life cycle undisturbed, because I have 5 acres of wooded property which is close to the Desoto National Forest. In a suburban yard setting, I imagine lawn mowers, dogs, fertilizers, etc. would tend to kill anything underneath the host plant.
Maybe if you have a remote area of your yard where nothing ventures, you'll eventually have success, assuming that you see red-banded hairstreaks in your area.
{{gwi:528469}}
Sherry

Sherry,
Strange... I live on three acres, surrounded by farms and just a stone's throw from the ocean and the Great Dismal Swamp... I have never seen a Red-banded myself but it's often photographed and printed in our local paper. I have a hedge of wax myrtles surrounding my land; only thing underneath is poison ivy :-0

Ironically, I grow the same lantana in your photo--maybe you can send some of those little guys my way?