A small study showed that levothyroxine is better absorbed at night. The thought behind this is that bowel motility is slower at night, thus increasing absorption. Also, most T4/T3 conversion happens at night and the stomach is definitely empty (unless the person succumbs to middle-of-the-night munchies
I've always taken my levo around 11PM, definitely at least 2 hours after last food/drink other than water.
I take my 1/2 of my liothyronine (generic Cytomel) at 8AM and the other half at 2PM.
If you decide to switch to dosing at night and don't feel relief from the sleepiness within 6-8 wks., it would be a good idea to look at your labs to see if your levels are too low.