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If you are seeing blossoms but you get no fruit, this could be a pollination problem. You can hand pollinate with a small paintbrush. Just go from flower to flower and swirl the brush inside the blossoms.

If it died all the way back to the root stock, there is a good chance that the root stock is what is growing now and not your lemon tree. Root stock trees are typically used because they are hardy and they often produce little to no fruit that is inferior in quality anyway.

As the new growth look very different from the way it was, I think it is safe to say that your tree actually died and this is the root stock. I would recommend starting over with a new tree.

The average lifespan of a lemon tree, especially its productivity, is 10-15 years. However, there are many types of citrus trees that may actually live up to 40 or 50 years.

This article should help: https://www.gardeningknowhow.com/edible/fruits/lemons/how-to-grow-a-lemon-tree.htm

There are a few reasons this can happen. The most common is that it is getting uneven watering. Citrus trees will drop their fruit first if they do not get enough water, even for a short period and they need more water when they are in fruit.

Pollination issues may also be the cause. If the flower is under pollinated, the tree may abort the fruit. A small paintbrush swirled in some of the flowers can help improve the pollination.

The requirements for lemons are very similar to that of limes. If you have not read it yet, this article may also be helpful: https://www.gardeningknowhow.com/edible/fruits/lime/reasons-and-fixes-for-lime-tree-not-producing-blossoms-or-fruit.htm

This article will tell you how to grow a lemon tree. They are all propagated in the same way:
https://www.gardeningknowhow.com/edible/fruits/lemons/how-to-grow-a-lemon-tree.htm