To dream of an iguana represents your fear of someone who makes you feel that you aren’t important. Fear that you have to put someone else’s needs before your own or face serious consequences. Fearing having no escape from someone dominating or intimidating. Fearing never being let go.
Alternatively, a pet iguana in a dream may reflect your use of fear to keep someone close to you. Scaring someone that they have no choice but to have you in their life.