The 360 version of GTA V comes on two DVDs. One is an 8GB "install disc" that you must install, and a second one is a "play disc" that you use to play the game. (The PS3 version comes on a single Blu-Ray.) As you can see in this video up top from Digital Foundry, the 360 version with the play disc installed to the hard drive is noticeably laggy compared to the off-disc version. It's not a huge deal, but the lag is present.
Fortunately, the same folks at Digital Foundry have already found a solution: If you want to play GTA V on Xbox 360 without the noise of a spinning DVD, install the first disc on your 360 hard drive like you normally would, then install the play disc to a USB thumb drive. They're sure to point out that your your mileage may vary depending on your thumb drive, but say that the approach made their lag problems go away.
See a demonstration here: