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Very few of the Lane Late flowers will produce fruit. Therefore, if you wait until the bloom is over to remove the new (if any) fruit, you will have a much easier time doing so.
If you want a fruit to mature on the tree, and still let the trees highest chance for good growth, you can leave one fruit on the tree until it matures. This is because all citrus draws its energy to grow and ripen from only the three closes leaves to the fruit.