Jolt, I'm probably only 1-2 mph faster on my carbon bike than my steel bike. On a typical 100 km (~65 mile) ride I probably average 11-13 mph on my ~20 lb. steel bike (Bianchi Eros Donna) compared to an average of 12-14 mph on my carbon bike. So I'm only a little bit faster on the carbon bike, but because it's also much lighter and more responsive, I'm usually a lot less tired after riding the carbon bike compared to the steel bike. I probably wouldn't be able to do century rides on my steel bike, but I'm usually OK after one on my carbon bike.
Now I use my Bianchi Vigorelli as my commuter bike, so with a rack, bag, and fenders it's closer to 27-28 lbs. After a week of commuting on my steel bike, I always feel like a superhero when I ride my carbon bike on the weekends. I'm guessing you'd probably have an even more pronounced experience if you rode a carbon bike compared to your 30+ lb. LHT.