The good thing about LED lights is that they are so versatile you can purchase LED lanterns, tent lights, flashlights, headlamps, and even LED light bulbs. Utilizing LED lighting you would be able to cook, clean, read, or do many other activities at night. Batteries are going to be your best friend when using LED lights and having some rechargeable batteries along with a solar charger would be good to ensure you didn't run out.
During an emergency in an apartment having a light source at night would be an important part of your preparedness plan. The sun would provide light during the day but at night without electricity you would be on your own for a light source. There are a lot of different options for off grid lighting but I think the best option is using LED lights. As mentioned before LED lights require very little energy and never need replacing.
A good LED lantern would light up a whole room, so would a LED tent light. A LED headlamp is one of the most handy things you can own and would allow you to have light and use both hands to cook, or read at night. If you have a propane lantern that is an option but those do emit carbon monoxide so some ventilation would be necessary if using one of these. Candles are also a good option so having some emergency candles stored up would also be a good idea. You want to keep your options open so LED's are great along with regular disposable batteries and rechargeable with a solar charger.