Q: Would a major leak from my exhaust back box cause it to fail the emmisions test and LAMDA reading

Hello - while an exhaust leak can have a minor effect on emissions, I would not expect that to cause a "Fail" - UNLESS your state or metro area does tolerate an exhaust leak for safety reasons (carbon monoxide poisoning for example). The inspection rejection notice should indicate whether unacceptable levels of hydrocarbons or oxides of nitrogen were the cause (or some other issue) were the cause of the failure. This information will instruct what problem area to pursue to correct the failure. Check for any problem codes, whether the Check Engine light is on or not. These will guide diagnosis and repair. If you need help detecting and repairing a leak, a qualified technician from YourMechanic can assist you with this.