What is the ruling of Islamic law concerning lying about the true identity of the driver responsible for a car accident to avoid punishment, and what should one who has done so do?

The basic principle is that lying is forbidden unless there is an overriding benefit. So, if a person is not known for recklessness, it is permissible to support their lie to avert punishment from them, in order to cover a Muslim's fault. However, if they are known for recklessness and violating laws, it is not permissible to support their lie, because covering for them would embolden them to فساد (corruption/mischief). In this case, you should inform the authorities, unless you fear harm befalling you.