2 ceiling lights were removed leaving a very smooth surface where the holes were repaired. The surface of the rest of the ceiling is somewhat ‘bumpy’ for lack of a better word. How can I get the repaired surface to have the same texture as the rest of the ceiling?
If you mean the rest is Textured Finish… get a Texture Repair Kit from your local paint store, take it from there… most likely you'll need to repaint the entire ceiling afterwords…
How can I get the repaired surface to have the same texture as the rest of the ceiling?
It really depends on the texture you need. There are several "kits" available that might work for you. These can be purchased at your local paint or hardware store. For mechanical textures, orange peel and knockdown, you can use a texture spray can. Hand textures will take some finesse.