The luggage allowance for US/Canada-bound flights on most airlines are usually 2 pieces of 32kg, irrespective of class of service ticketed. In most cases, you don't get any extra weight allowance for flying in First or Business class, on flights to/from US/Canada. (Various airlines are trying to change this generous allowance, but not too much has changed yet)
However, if you're flying on First or Business then the check-in agents are that much more likely to turn a blind eye if you have an extra piece. Also, elite tier of the frequent flyer programs tend to give extra luggage allowance (for example, United Airlines Gold (Premier Exec) will get to check in an extra piece, bringing the total to 96kg total)
Note: Due to H&S at British airports, you are no longer allowed any single piece of luggage that exceeds 32kg unless exceptional prior arrangements are made. Apparently the baggage handlers don't like lifting heavy bags.
I'm not sure about 1lb but if it's anywhere like 2kg over the 32kg per piece limit (i.e. 34kg+) then you are 90% guaranteed to be told to bring that piece down to below 32kg.