Fired for the 2nd time in a row. What should I do?

I'm 20 years old. The first job I had in high school was a custodian, and I hated it. I got fired after a year for asking for a different position. I was able to lie and say I got "laid off" to get a new job, also in retail. I've been working that next job since I was 18, and never had a problem until the past month when a new manager was hired. I was late twice in one month, so he fired me (even though I've been a good employee for 3 fricken years, and I was only late because I was without a car for that short time! Yet he couldn't get that through his head.). Now I need a part time job this summer to pay off some debt. I'm also a college student. Should I even bother stating my work history on my job applications? I'm just going to apply to basic low-end jobs like grocery stores and jobs at my school, so I doubt they'll REALLY care if I even have a job history or not.