Hi, and welcome. First may we ask you to tell us where you are? This gives us some info on the strength of your sunlight and the humidity of the air as well as how cool it gets at night if the plant is right next to a window. If you fill in the area in your personal profile (the little person in the blue sidebar to the left there) your city and state or country will appear in the upper right corner of all your posts automatically.
Could we also please see a picture of the whole plant, including the pot? The solution maybe as simple as just a new slightly larger pot, with fresh potting soil. From your first picture, that pot looks to be pretty small. Citrus trees naturally have a wide-spreading root system with their roots fairly near the surface, so a wider, shallow pot might suit it better. If you can just slip the plant out of the pot it's in, and see if the roots are crowded, and going round and round inside there, that will tell you it's needing a new pot.
First problem I see is the yellow leaves with dark veins. This usually indicates iron chlorosis. Have you fertilized your lemon tree at all since you got it? If you did, what did you use?
Second thing, and this may be only the quality of the pictures but the leaves look a little bit spotty to me. You might have some spider mites making themselves at home on your plant. The solution for this, and it will be good for your plant anyway, is to put it in the sink (or better yet in the shower) and give it a nice brisk shower with lukewarm water every week or two. This will wash off the mites, any aphids that may be around and also give the plant what it would get outside in nature - rain! Be sure to spray the undersides of the leaves as well as the trunk and the soil surface, too.
I hate to say this, but you really should remove the fruit from that baby tree. It's in distress and having to put a lot of energy into making fruit is a big demand on it. Even here in Florida where we grow lots of citrus outdoors, if you plant a new tree, you're supposed to remove all fruit for the first year to let the plant develop a strong root system and more foliage.
