Can a leased car be included as part of net worth? If so, how?
I wouldn't think so. It has no positive value. It is in fact a liability.
You owe a specific amount of money per month as a payment for the lease. You could owe additional charges at the end of the lease for excess miles or above average wear. If you need to get out of the lease there could be a penalty.
At the end of the lease period you have nothing, except an option to buy the car. Which may or may not be a good deal depending on the exact terms of the lease contract.
It does need to appear in your budgeting, and insurance is needed to prevent the liability from blowing up in your face if something happens to the car. You might also need insurance to make sure you can make the payments if you are unemployed or disabled. Though those risks are similar to a loan.