There was some research for soybean oil as a control for aphids on daylilies. There are details here:
http://botanicaloils.tennessee...
BTW most of the time aphids give birth to live young rather than lay eggs, that includes both winged and non-winged females - most aphids are female. They're more likely to switch to egg-laying late in the year but there are a number of different aphid species that can affect daylilies I don't know how much the lifecycle may vary for each.
