The torque converter doesn't usually drain out, which is why a mere change in sump fluid doesn't refresh the torque converter's fluid -- you have to pump it through, with a hose (like the one IPD sells, or something similar).
But when you have the first-thing-in-the-morning lag, is usually means that fluid isn't yet circulating through all the passages of the transmission, energizing the clutches (or what-have-you). That's why I thought, low fluid level.

Forgive me for asking, but did you take notice of the different temperature scales on either side of the dipstick (i.e., "hot" vs. "cold"). It take a LONG time to get the fluid to heat up to be appropriate for the "hot" scale -- usually a half-hour or more of fast driving, in fall or winter; less than that, you should be using the "cold" side of the scale.

Another way (some here will disagree, but I've found it to work consistently with "engine running" measurements):
After leaving the car overnight, you can check the fluid "cold" without the engine having been started -- pull the dipstick and reinsert (this pull out and reinsert is important), and then see if the fluid is up to a rectangular notch higher up on the dipstick, above the plastic "scales" at the end of the dipstick. It should be there, within that rectangular notch, when the fluid is "overnight" cold, and without the engine having been started. But if you start the engine, even briefly, don't use this method until the following morning.