Lacewings are actually beneficial predators that feed on various insects including aphids.
Not sure is this is oily substance - possibly an oil produced by the plant that may be on the leaf surface due to high temperatures. If it is sticky, it could be honeydew from a sucking insect like aphids and the lacewings are coming to help you manage them. So best not to kill them. https://www.vegedge.umn.edu/pest-profiles/beneficials/green-lacewings

Hi again,

Not lacewings.  Lace bugs.  They are a sucking insect. 

I'm thinking this brown stuff is  wet alternaria or septoria fungus infection.  The photo was taken after a rain fall, and some of my sunflowers in another area have brittle brown areas with gray raised bumps in them.

Sorry about that. I also was looking at the clear substance on the leaves (apparently water).

This looks is a mildew caused possibly from water splashing on the tips of the leaves or the leaves touching moist soil. I see a little white white moldy growth near the tip and underneath the leaf. Not sure how you are watering, but uUse drip irrigation (vs. overhead) and then mulch the soil to prevent rainfall from splashing soil onto the leaves and  to keep leaves dry.

I don't water them much at all, to be honest. They haven't needed it. This particular leaf is about 3' off the ground, so I don't suspect soil splash, but I have fungus issues throughout my property, and I'm sure it's blowing everywhere.

I removed this leaf and another that was showing similar symptoms in that area and have not noticed any new instances of this water-logged appearance, but as I said, I have been battling a (possibly related) leaf blight of some sort on other sunflowers (and several types of plants) in different areas of the property. I always prefer organic solutions, but have been forced to resort to fungonil for my tomatoes, and thought I'd see if it had any effect on the sunflowers (and my echinacea, which also seems affected).

Attaching photos of a different sunflower leaf and an affected echinacea leaf. Wondering if that waterlogged area from my initial inquiry is just a wet version of these same brown lesions?

Without sending these to the Plant Disease Clinic, we can't be sure, but I feel they are leaf spot diseases caused by bacteria or fungi that have become more prevalent this year thanks to the hot and humid weather we've experienced recently. Sanitation is helpful - removing infected leaves - as well as increasing airflow and light by planting less densely. However, it's too late for that unless you choose to remove the infected plants.  

So ... being that these are annual plants, I don't feel sending a sample is economical at $45 per sample. But I would recommend mulching the soil, cleaning up fallen leaves and planting perhaps less densely and in a different location next year. If you are growing these for $$$ (oil, cut flowers, etc.) and if you grow them every year, perhaps a sample would be a good idea. Your call. If they were my plants and planted just for fun / flowers in my garden, I would remove the damaged leaves and possibly a few less impressive plants that may be the worst offenders, and enjoy the flowers in a vase.