This is a tricky one since the piece concept applies from the Americas but, on CX, the weight concept applies from Europe.

Are you on one ticket? If so then the piece concept should apply for the whole journey and even if you do have to pay for a third piece the price should not be too high. Maybe a couple of hundred dollars.

If you are on separate tickets there may be a problem. CX may apply the weight concept from LON and if your three pieces together are under the total weight allowance then you will be fine but if your three pieces each weigh 32kg you may be liable for a lot of money in excess baggage fees.