"is it against the law if you choose not to take a lunch to
make up for lost time on your payroll"

"is it against the law if you choose not to take a lunch to
make up for lost time on your payroll"


No. It will be up to your employer's policy on how they handle paid breaks and lunch periods. While many labor issues are mandated by the law, others are Company Policy and you would need to find out your company's policy on this issue.
NOTE:
The law does not provide employees with an explicit entitlement to a meal period. Each agency has the authority to establish its own requirements for meal periods. An agency may require or permit unpaid meal periods during overtime hours, and the policy may be different from the one for the basic workweek.
For example, an agency could permit employees to work 8 overtime hours on a Saturday or Sunday without any requirement for a meal period. In exceptional circumstances, an agency may permit employees to eat their meals while working.