My company refuses to pay for time worked during lunch.
Therefore, you are entitled to be paid for all time worked. You can report not being properly paid to the Department of Labor (DOL). You can obtain the information that you need to do this through a DOL website in most states. Normally, the DOL will see to it that you are promptly and properly paid.
However, a couple of things to consider: Does your company handbook specify that only pre-approved overtime will be paid or that all non-exempt employees must clock out and take a full X minutes for a lunch break? If either is the case, it does not mean that you are not entitled to be paid for the lunch time that you worked. But it does mean that your company management may feel that it has a legitimate reason not to pay you for this "unauthorized" work time.
So rather than report the affront to the DOL, you may want to check your employee manual. If you did violate a defined policy, approach this differently. Go to your company management and admit that you did not know about the rule but will abide by it going forward. In the meantime, tell management that you would appreciate being paid for the time that you already worked instead of taking time off for lunch for the days in question.
Keep in mind that determining work hours is the responsibility of company management. You were being unreasonable in thinking that you have the right to simply decide to work more hours and expect management to pay you without prior approval.