You did the right thing with the removal of the lemons. If it had lemons on it in the first place then it was a stressed tree. When they stress they produce fruit. When selecting citrus, choose one with healthy leaves, a good shape and no fruit. Or few fruit at least.
However, get some seaweed or kelp extract and give it a drink at the rate recommended on the bottle. Give it another one in a week or so. I'm assuming you watered the plant well before and after transplanting and that the potting mix is moist, not water repellant and also that you planted it at the same depth it was before. If you only bought it recently, i'd be tempted to take it back to the nursery and quiz the 'master gardener'. Good luck.

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The secret is the soil.

The tree now has two tiny, tiny new leaves, but they must have been there before-would it have new growth in only a few days
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OK. As long as those leaves are there it should be OK. It went into some kind of shock from the transplant i'd say. Your timing to transplant, ie the end of Summer, isn't great but it'll probably be OK. Try the seaweed and don't feed until the new growth becomes more evident. You may get no more for the year but don't panic. You may get some flowers again in Autumn. You know what to do!

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The secret is the soil.

I bought a Meyer lemon and when it arrived the leaves looked too yellow. I gave it Espoma Natural Traditions Garden Iron which is 55% sulfur. It is doing beautifully now. I know that isn't the same as your problem but in the future you might consider giving it some of that.

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gailo