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Certainly there is. What you will notice is that it will take longer for the fruit to mature when it spends part of its time indoors, but it is a small price to pay. Also in order to keep the fruit on the tree, it is VERY important to make sure the tree stays watered. If it gets dry at all, it will abort the fruit first.

On citrus trees, I would recommend removing any suckers that grow from the rootstock. Most rootstocks for citrus trees are inferior trees and their suckers will only sap energy from the tree without ever producing fruit.

Curling leaves on lemon can indeed be caused by stress. I don't know how close you are to the shore, but if you put your lemon tree so that the house is protecting it from salt wind, that is the most you can do. This article will give you some more ideas on leaf curl: https://www.gardeningknowhow.com/edible/fruits/citrus/curling-citrus-leaves.htm
Also some tips for potted lemon trees: https://www.gardeningknowhow.com/edible/fruits/lemons/growing-lemon-trees-containers.htm

To identify suckers, find out where they are coming from. If they arise from the roots, the base of the tree, or anywhere below the graft union, they would be suckers from the root stock, and should be cleanly cut as close to the tree as possible. https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-sucker-removal-and-tree-sucker-control.htm
If the branches are emerging from the tree above the graft union, or from any of the side branches, they are branches from the tree. A sign that your tree is healthy, growing roots, and sending out new branches. Your tree is still very young - meet it's cultural requirements, and it should soon start fruiting. https://www.gardeningknowhow.com/edible/fruits/lemons/lemon-tree-not-fruiting.htm

If I understand correctly, your lemon has been fruiting well, until a couple of years ago when the fruit started to drop, and this year it's not even flowering. If you've been fertilizing all along, it seems most likely that either water or light has changed. One thing, have you been increasing the water as the tree grows? The other thing which I'm thinking is that other plants have been growing and shading the lemon more and more; this would make the lemon fruit less and less as years go by. So you can try providing more water, and trimming other plants that may be shading, and follow up with the information in this article: https://www.gardeningknowhow.com/edible/fruits/lemons/lemon-tree-not-fruiting.htm

It sounds like the problem is uneven watering. Citrus trees are deceptive in that they will not lose their leaves due to being to dry until after they have been watered after being too dry. Early loss of fruit is also a sign of the tree not having enough water for a period of time while in fruit. I would make sure that the tree is getting enough water, all the time. Also, remember to increase water to the tree while it is in fruit, as its water needs increase. This article may help as well:
https://www.gardeningknowhow.com/edible/fruits/citrus/leaves-falling-off-citrus-tree.htm