Maximum bombload of the Lancester was about 5,6 tons, maximum bombload of the He 177 was 7,2 tons. End of story...
You've never heard of the Grandslam, 22000lb bomb!!!
Lancaster range with bomb load
Range
2530 miles with 7000 pound bomb load
1730 miles with 12,000 pound bomb load
1550 miles with 22,000 pound bomb load
Avro Lancaster Specifications
Here's a bomb load matrix:
Bomb Loads
loads of 13500 to 14000lbs were common.
Regarding a hypothetical A-bomb Lancaster, a Lancaster could have taken off from Tinian and landed at Okinawa, or alternatively, the Lancaster could have used air to air refueling:
Unreal Aircraft - Flying Forever - In-Flight Refuelling, WW2
as the RAF had perfected this technique at this time. Most speeds given for Lancasters are with bomb loads and full armament. Aircraft of WW2 by Chant,p36, states a top speed of 345 mph for a Mk VI with all armament except the tail turret removed.
Regarding importance to the war effort, the Lancaster dropped " 608,612 tons of bombs in 156,000 sorties" considerably more than the B-29, as the total tonnage dropped on Japan was "159,862 tons of bombs " .
HyperWar: Strategic Air War...Germany Japan [Chapter 1], p256.