Your employer should have instructed you to clock out by the 5th hour of work for at least a 1/2 hour lunch break. That is the law. You don't state details such as whether you were instructed to work longer, or were not provided with relief to take a lunch break. It also depends on the type of workplace, such as office versus restaurant, etc... that may make a difference.
Statutory authority regulates your lunch breaks. The issue becomes very muddled when or if you voluntarily do not take the lunch or break when you have a right to take said time off. It is different than if your employer is prohibiting you from taking your lunch and/or breaks in a timely fashion, which would be actionable. If there is no such prohibition, and you are electing to take such action by and through your own elective decision, then your likelihood of success is rather dismal.
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