I also had three children in 31/2 years. Let me assure you that when they're teens, it's a good thing, and I'm alot happier to be seeing the light at the end of the tunnel than my friends who have kids in highschool and preschool at the same time!
I was a liar pretty much up until I got married. I am an oldest child and oldest grandchild and I started lying for the usual reason (so I wouldn't have to brush my teeth) and got worse because I wanted attention and I'd lie to pretend my life was the way I wished it were. I lied to new people automatically so they'd think I was richer, more popular, etc. than I was. I quit when I got married and started living the life I wanted to have, and then later when real life intruded(!) I was out of the habit and mature enough to realize that lying about my life wasn't going to make anything better.
So I think she probably feels some lack of attention. Most of the lies you name are attention getters (are her classmates new this year?) Also, lying about eating dinner when you don't want to eat it is very normal for the age. You don't want to let her get away with lying, but right now, she's being rewarded for it with your attention. My minister told me once that I didn't care if the attention was good or bad as long as I was getting it, and he was pretty much right. So since you don't want to let her think the lying is okay, the punishment needs to be swift and short, and it might be that instead of having a big long talk with her about it, you should say "Mommy is upset with you when you lie, and I need to spend time away from you now, so go to your room for a time out." But the most important part is that when she is not lying, be sure to pick things that please you and spend time talking about them "I really love how you arranged your dollhouse, can I play with you for a few minutes?" Also, arrange some parent/child alone time for her like a trip to the park or McD's for lunch, or a Big Girl story time after the little ones are in bed. If she gets her attention for being good or just for NOT being bad, she's more likely to try being good.
But I gotta say I LOVED the nailing the sins on the cross. That is so powerful for that age.
Oh, yeah, I also want to point out that even though I lied alot, I never was in trouble much and did well in school and worked for a living and married pretty well, and am now a pillar of my church with Christian teens, so while you need to work on it, don't worry too much.