Firstly, Lamictal is not approved by the FDA for treatment of any anxiety disorders. When Lamictal went through clinical trials, anxiety as a side effect was reported by 4% of participants - but 3% of the control group also reported anxiety, so this would be considered a rare side effect. Even though treatment of anxiety isn't an approved use for Lamictal, some doctors do prescribe it to patients who have conditions such as Generalized Anxiety Disorder and Social Anxiety Disorder, among others.
There is no concrete evidence that Lamictal helps with anxiety - and also none that it causes anxiety to any great degree. I found some blog and forum posts by individuals who said Lamictal helped their existing anxiety, and others who said it caused anxiety. And I found no clinical studies addressing the issue. Thus, it's impossible at this to gauge Lamictal's effect on anxiety.
For more on anxiety disorders see Anxiety Attacks and Anxiety Disorders.