I have caught Lacewing at the same moth trap but they are nothing like this oddball - they don't have alternating black/white antennae, the palps are much smaller, the wings are clear with very distinct veining and larger and they are held against the body very differently. I attached a sample as well as some closeups of the head/thorax areas, notice the large palps and the fuzzy head.

Is it alive in the photos? Any side views? Do you still have the body? I can't tell from the photos but I'd start by ruling out caddisflies.

Some interesting similarities in the Psocoptera; haven't found a good match yet.

Psocoptera Copeognatha is close but no cigar, wing color is similar but abdomen protrudes beyond wing tips, legs and antennae are wrong. Thanks for the new lead.

Long-Horned Caddisfly, keyed from:

http://entnem.ifas.ufl.edu/bug_club/bug_ID/34.shtml

(not to unrule Fori, but the key led me here)

Identified from:

http://bugguide.net/node/view/53447/bgimage

Genus Nectopsyche; common name "White Miller"

Nectopsyche pavida and Nectopsyche candida are very similar, with N. pavida being my guess. It is very odd that I get so many aquatic insects at my moth trap, there are no streams or bodies of water within a 1/4 mile or more, yet I get Water Boatman, numerous Caddisflies, and Stone flies. The only water in my back yard is a bird bath. Thanks for the input, it is greatly appreciated.

Yes, one of those two species. Candida somewhat more widely reported than Pavida; all 4 species of the genus have MI distribution.