If I got into an accident and it was fault on the other driver, my insurance lapsed 3 days prior; will his insurance still cover the payoff of my car?

You should be asking these questions of your attorney; you hired him/her to represent you and they need to. Assuming your attorney does not return your communications, the answers are: 1) your lack of insurance only matters as to the law that states if you are uninsured you can not collect anything for pain and suffering; 2) insurance policies normally have a 30 day grace period so that you are still covered up to 31 days after the date your last premium was due; 3) insurance companies only have to pay the lower of either the value of the car just before the impact or the cost of repair [check to see what your car loan agreement says, if anything, about what happens in a car accident]; 4) you can file a complaint with the State Insurance Commissioner that the other carrier is not acting to try to resolve the case [but he can not force them to settle] and; 5) your attorney will get the insurance carrier to pay more of the DC billing [and get the DC to reduce how much you have to pay him back] than you could and might get more of a wage loss and car rental claim then you can, but that is relatively easy and not too time consuming but you will be paying 1/3 of the settlement for that [most attorneys do not charge for the property loss claim; unless your injuries end up with a high medical bill [insurance companies dislike DC's], the case probably is not worth much to the attorney as to fees so the case will not be among those with priority.