Ask Mr. Smarty Plants

A Lantana tree in a cold climate has come up before with Mr. Smarty Plants, you can follow this link to read the whole answer: previous answer . Quoting from that:

"Here is a picture we found when we Googled "Lantana Tree". This is probably a cultivar or selection of the native Lantana urticoides (West Indian shrubverbena) which has been pruned and trained, in greenhouses, up into a tree form. There are many hybridized types of lantana and some non-native, although this one is native to North America. All of them, however, are tropical to sub-tropical in nature. In Texas, in all but the southern part of the state, its branches will die back in the winter and emerge again in the spring."

Since lantana is a full-sun plant, that morning sun, probably through a window, is not sufficient, and that could be the problem. Also, the green leaves dropping off sounds like too much water. Is your plant getting good drainage? It should be in a pot with a drainage hole, and the roots should never be standing in water. If you are not seeing any insects like whiteflies or aphids on your tree, the problem is almost certainly cultural. We would recommend you let the tree go dormant, since they do that ordinarily anyway, cut back on the watering, perhaps giving it a good deep watering only about every couple weeks while it's inside. Then, as soon as you have passed your last average annual freeze date, move it back outside, into the sun and start watering and fertilizing again. We really can't guarantee that it will come back in the Spring, but it's a tough plant. However, you are asking it to flourish in a climate and environment where it was never meant to be.