Lemon Eucalyptus Looks Withered

I have a lemon eucalyptus plant in a small pot that I keep indoors, since I live in New York, NY, USA. It has many branches but many of its leaves are brown on the edges and curled up, and the plant itself just looks like it is half alive. I tried giving it fertilizer but it did not seem to make a difference. I water it about once a week. During the day I have it by the window, but the sunlight is usually very weak. Is there anything I can do to improve the growth of the plant? I don't know if the plant needs more warm light; I have a reptile light but I don't want to use it if it will hurt the plant more.

Eucalyptus do not want to dry out completely.(And they hate root disturbance) The former can easily happen if you keep the plant in a small pot that you water only once a week. The leaves probably reached a transpiration rate that could no longer be made up with the water supplied and on drying out many roots died...and a viscious ncircle started.
I would suggest you move the plant into a bigger pot, WITHOUT disturbing the roots, put a large plastic bag around the plant that you leave open a crack at the top and keep the soil evenly moist, but not soggy. When healthy new growth starts, gradually open the bag more and more, until it is finally all removed. Take about two weeks to do this.
If the potting on produces no results in about a month, then cut off about one third of the plant, before bagging it again.Hopefully by about a further month, new growth will have started.