Meh, help section might have gotten you a faster response... I'm not much help since I don't play TF2 but if I had to guess I'd blame your computer. I always thought servers that are good and stuff are typically run by a server box or a computer specifically for said server. Trying to play on the server, even though it's just in the TF2 game, is still stressful on your computer, it probably costs a lot of resources for your computer to play and run the LAN server even if you're the only one in it. I dunno how good your computer is though so maybe it's not even that... Those are just my 2 pennies.
I prolly have no idea what I'm talkin' about since I don't know much about TF2 but yeah... Hope this helps and sorry if I'm completely off the mark xD.
Regards,
~Red