Possibly. You have taxable income if the settlement is more than you paid for the car, not counting finance changes. That is not necessarily the same as what the finance company wanted for the remaining value.
For example, suppose you leased a $40,000 car. The residual amount (buyout amount if you wanted to keep the car at the end) was set at $25,000, so you technically agreed to buy the first 2 years of the car's life for $15,000, plus whatever the lease interest rate was. Suppose the accident happened right at the end of the lease. The lessor is going to want their $25,000, plus a bit, more or less. If the insurance settlement is $30,000 where you get $5000, its not taxable because your original cost was $15,000.
On the other hand, suppose the accident happens halfway through the lease, and the settlement is $35,000. At that point you would have paid about $7500 for your share of the car. If $25,000 goes to the lessor and $10,000 to you, then $2500 is taxable (the amount that is more than you paid for your share of the car).
