My RCA television has no picture

Need a little more detail than that. What make/model? What happened to make you think it was the lamp?

If it is a projector it is certainly possible the lamp is the problem as that is common. For most TVs it is fairly easy to replace the lamp. Usually there is a panel on the side with a screw or two that you remove and pull the old bulb/housing and replace with a new one. Most are pretty much plug and play. Lamps run anywhere from $100 to hundreds of dollars and average life is probably in the 2000-3000 hour range so it may not be worth it with HDTV prices continuing to fall.
 
Need make and model, the methods and trouble shooting in which you fix Projection, CRT Projection and LED Projection are much different.