Certified GKH Gardening Expert
It is not necessary to pick the fruit like that. By the time they are able to fruit, they should be well established. The only reason I would say to pick the fruit like that would be, for some reason the tree isn't as full of leaves or branches as you would like.
Here is an article about when to harvest: https://www.gardeningknowhow.com/edible/fruits/citrus/citurs-fruit-wont-come-off-tree.htm