To eat, or not to eat?

[DTill]

I work third shift full time as well as go to college full time. Here is a run down of my day, in a nut shell:

3PM Wake up
3:30 PM Lift
6:00 Classes
11:30 PM Work
8:00 AM Sleep

I've read its terrible to lift if you havnt ate anything in the day. The crappy thing is I really dont have time to move my work out to any other part of the day. Its either work out right when I get up, or not at all. So, should I eat before I work out, and be lifting with food in my stomach, or just skip the food all together and eat when I done? I try to drink a whey shake when I wake up, figured because it digests fast it would help for the workout that follows.

Any ideas?