The extra weight of the 20" rims opposed to the 18" rims does take alot more power to turn over. The biggest problem is the lowered gearing you now have. Those 20" tires have given you less gear multiplication then when you had the 18", unless you managed to go with a tire with 2" less sidewall - but harsh riding and...the Lightning had thin rubber to begin with. You would need some form of a gear swap to correct your loss of 1/4 mile time. Or you can do some mods to make up for the lost gearing. You did notice lower rpm's when cruising on the interstate, right?
The taller the tire is, the numerically lower the final gear ratio will be. If you have 3.73 gears and a 28 inch tall tire and then put a 31 inch tall tire on the same vehicle, it will slow the RPM range down accordingly. If you go on the freeway and have a friend drive next to you at the exact same speed (cause your speedometer will be off unless you have the capability to reprogram your ECM) with the different sized rear tires and you will see that the RPM on your trucks at the same speed will be different. I don't know the exact RPM but it will be higher with the shorter tire. Now, do an "acceleration challenge" next to your friend (not saying drag race, that's illegal and I NEVER break the law!!!) with the two different sized tires and you should notice that you will accelerate faster with the shorter tire. If you want to keep the same wheel/tire combo you have and want the accelation back, you will have to do a gear change.
I have 4.10s in my truck and absolutly love them, but I also still have the stock sized wheel/tire combo and my truck came equipped with 3.55's.
As far as how much it will affect your et at the drag strip, it will definatly affect it but as to how much, I cant say because there are so many different variables that will affect it. You also have to consider that a taller or wider tire will also have more rolling resistance as there will be a larger contact patch on the ground. And like Saurian said, there will be a substantial amount of wieght added to the whole wheel/tire combination. Wieght, especially "sprung" wieght, will have a big effect on your vehicles performance. Thats why I need to go on a diet!!