Here's my laptop:
http://www.newegg.com/Product/Product.aspx?Item=N82E16834220733&nm_mc=TEMC-RMA-Approvel&cm_mmc=TEMC-RMA-Approvel-_-Content-_-text-_-

When I ran the game for the first time it recommended High settings, but regardless of the settings I choose, after some amount of time (usually 5-10 minutes) or running smoothly, everything gets really, really laggy. What's up?

Sounds like a memory leak to me. Have you tried the beta nvidia drivers that were recently released?

Actually it does sound like a Memory leak.

Framerate issues, not lag. Lag is online latency.

Make sure your laptop is running on the correct graphics card. Many people with gaming laptops seem to be oblivious to this. Open up the Nvidia Control Panel and under 3D Settings/Manage 3D Settings click "Program Settings," then Add both TES.exe and TESLauncher.exe to the list and make sure it's set up to use the High Performance Graphics Card.

Have you checked the temperatures your system is reaching while running the game?

Many laptops have just barely adequate cooling and the right kind of load could make the thing overheat after a few minutes.