No you can not lag in singleplayer.
All orders are issued imediatly as you give them cause there is nothing to delay it.
The closest you can get to lag in singleplayer is if your frame rate drops into single figures, the mouse loses responsiveness and orders can take a few frames to issue cause the interface is updated ever few seconds.
You are probably confusing low frame rate with lag. Low frame rate is not lag.
Low frame rate is caused by some piece of hardware in your compuer bottleknecking the game so it can not run at full frame rate. This usually is the result of a badly made game (map in the case of WC3) or a game with to high system requirements for your PC.
Lag is when commands from the user are noticably delayed before the game aknowledges them. There are multiple causes to lag. The most common is a poor internet connection in syncronized multiplayer games, the result is that it takes a long time for an order to sync and as such you might have to wait many seconds before an order is carried out by the game. Another cause of lag is extreemly low frame rate, whereby the frames are comming so slowly that there is a cognitive gap between doing something and it happening on screen, however this is purly a side effect of the real problem as the orders are being sent instantly but are comming in slower due to the computer not coping with the game and so should be referd to as low frame rate and not lag (or atleast frame rate lag so as not to be confused with connection lag).
In warcraft 3, people get confused cause in multiplayer games you can get 2 kinds of lag happening.
Response delay is when the host is in a geographically bad position or has a bad connection and can not send out orders at a reasonable rate so orders can be put into que for up to many seconds before they are carried out. All the time the game runs normally, just you can not do usual tactics like kiting mobs or retreating from a battle (all ability to micro is lost).
Stuttering is when a player is in a geographically bad position or has a bad connection so can not update with the host in time (host is receving orders slower from him). The result is everyone in the game is put on hold until he updates making it look like framerate has hit 0 or very low numbers. If the bursts become bad enough, eventually you start to get the waiting for player dialog after a few seconds. Despite the whole game appearing to freeze and hang, the game is actually still running at normal frame rate and it is not caused by PC bottleknecks.
