I would like to know whether there is any difference between the following two terms which I think both refer to boiling: bollire and lessare.
"Lessare" refers to a way of cooking food by boiling it, whereas "bollire" has a more general use. For instance, you can say "l'acqua bolle a cento gradi"o "l'olio bolle a temperatura maggiore dell'acqua", but not "l'acqua lessa" o "l'olio lessa". Note that in those cases, "bollire" is an intransitive verb. But when "bollire" acts as a transitive verb and it refers to food, it is essentially synonym of "lessare": you can say either "far bollire le patate" or "far lessare le patate".
Another fact of the verb "bollire" is that it has some figurative uses that you can't express with the verb "lessare". For instance, you can say "bollire di rabbia", "bollire dalla rabbia", "bollire d'ira" to express that you are very angry, "avere il sangue che bolle" to mean having a passionate temperament or "qui si bolle" to say that you are suffering because is very hot.