Can a plant grow under a lamp?

I've have several house plants under a floor lamp on a timer for many years now. They do quite well compared to a couple I put in my hallway WITHOUT any lamp on them. The little daylight the hallway gets doesn't suffice and eventually any plant I've put there has died. But the plants under the timed floor lamp are too many years old for me to remember. I even have a cactus that is at least 10 years old under the lamp. I use to put it outside in the summer time but it's so tall I'm afraid to move it for fear of breaking it. I've also found that my plants seem healthier since I starting keeping them inside under the lamp rather than moving them outside for the summer.