I broke down and bought Scott's Ecosense Bug-B-Gone insecticidal soap for use on the lupins. The one plant is starting to come back but since there are no flowers on the plant the aphids are going after the new growth and killing it. The second plant also has a more-than-healthy aphid population that is rapidly reproducing. I found three sets of babies without even looking for them! I just can't squish them fast enough on either plant to keep them in check.
Aphids do have numbers on their side. During the summer when there's food to be had, their numbers increase exponentially by giving birth to live clone babies (aka parthenogenic reproduction), one after another. Interestingly, some unborn clone babies have their own unborn clone babies growing in them... which is kind of creepy when you think about it. All they do is eat, give birth, and poo out that sticky-sweet "honeydew".
From a "getting rid of them" perspective, as if their numbers weren't bad enough, lupin aphids also seem to be tougher than most aphids. Usually you can put the hose on aphids and their soft little bodies will be crushed. Lupin aphid babies are crushed easily by water but the comparatively huge adults (they're 3-4mm long and about half that width) just get knocked to the ground by the water and then they crawl back to the plant.
These aphids are so hardy and so fast-reproducing and are doing such bad things to our lupins that I figured it's time to try the insecticidal soap. We aren't allowed to use pesticides or herbicides here in our region so we can only buy items that are natural and won't (well, shouldn't) do damage to the greater environment. The stuff I bought contains only potassium salts of plant extracts and works on contact with the aphids - I actually watched them die as I sprayed them.
I hope this treatment works. if it doesn't, I guess I'm going to have to go up to something with pyrethins (a chrysanthemum flower extract). That stuff kills most insects, including the good ones, so I'd rather not use it if it's not absolutely necessary.