I believe Lakshmana was more agyakari than Sita. While going to 14 years vanwas Rama said Sita to stay back in palace, but she didn't. Next, when Lakshmana said Sita not to cross the lakshman rekha, she did crossed seeing a brahman asking for food/foodgrains. Third, when Hanuman said to Sita he will help her get free from the trap of Ravana in Lanka, she didn't agree and asked him to tell Rama to kill Ravana and then take her away. There are more such instances.