Lagging with myself?

All games on Battle.net 2.0 (which SC2 uses) are hosted on Blizzard's servers, hence your lag. Only when you are playing in offline mode are the games hosted on your own computer. You can play offline by selecting the "play as guest" option on the right hand side of the login screen instead of completing the normal login process. If you are playing in offline mode, then unfortunately you cannot earn any achievements.

Just because you aren't connected to other computers doesn't mean that your network isn't under strain. Before you start laying the blame on Starcraft 2 itself, consider the following:

• Are you on a wireless connection? More than once I've simply had a 'hiccup' due to my router being cheap and old (7 years now, I think?).
• Are you on a shared wireless connection? One of the joys of living with my brother means a constant awareness of what he's doing on the network. If he's playing online games, it's usually not a big issue, but heaven help my FPS and latency should he decide to open a youtube video or shudders with shame handling torrents.
• Is this a lag issue at all, or merely graphical frame stuttering? Either force your computer to ignore the internet (possibly hard, I realize) and play a custom game in Starcraft 2's offline mode. It's easy to check, and a good way to determine if it is the network, or if it's your computer. Alternatively, try playing Starcraft 2 from a separate computer.
• Wait a week and try again! Sometimes, there's just something wrong with the pipes -- momentary troubles either with your provider, the battle.net servers, or any number of things. If it continues to be an issue over a longer time period, then it is more likely to not be external problems.