What are the significant events and themes underlying Act 2, Scene 3, in The Merchant of Venice? What, for example, is the "heinous sin" Jessica refers to?
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As your original question acknowledges, the center event of the scene is Lancelot's departure from Shylock's household, and even though Lancelot is reluctant to leave Shylock's daughter, Jessica, whom he describes as a "sweet Jew," he cannot stand another minute in Shylock's house, as Jessica understands only too well:
I am sorry thou wilt leave my father so./Our house is hell, and thou, a merry devil,/Didst rob it of some taste of tediousness./ But fare thee well. . . .
Jessica, who is, by this point in the play, convinced of her father's greed and, more important, of his hatred of Christians (and, one could argue, justified hatred), is reluctant to see Lancelot leave but understands why Lancelot has made this decision, and she uses this opportunity to send a message to her lover, Lorenzo, so that they can elope. It is equally clear that Lancelot, even though he cannot stand being in Shylock's service, reluctantly leaves Jessica:
Tears exhibit, my tongue, most beautiful pagan; most sweet Jew; if a Christian do not play the knave and get thee, I am much deceived. . . .These foolish drops do something drown my manly spirit.
Lancelot's farewell speech accomplishes two important tasks: it confirms that Jessica is an "acceptable" Jew, that is, she is not like her father--the implication is that she is closer to Christianity than to Judaism--and Lancelot foreshadows the elopement between Jessica and Lorenzo. And Lancelot's main purpose, once he leaves Shylock's house, is to give Jessica's note about the elopement to Lorenzo, which leads to Jessica's formal rejection of her father and her religion.
At this point, the reader clearly understands that Jessica (even though she is a Jew) and Lancelot represent the Christian side of the struggle against Shylock, who represents the English stereotype of the money-grubbing enemy of Christians. Shakespeare's representation of Shylock plays into the Elizabethan view of Jews as dangerous outsiders, bent on the destruction of Christians in any way possible--in Shylock's case, he uses his money as a weapon. Jessica and Lancelot, in this scene, are at the Christian end of this spectrum.
Jessica's last speech makes her Christian conversion quite clear:
Alack, what a heinous sin it is in me/To be ashamed to be my father's child!/ But though I am a daughter to his blood,/I am not to his manners. . . .
The "heinous sin" is not that Jessica is a Jew but that she is denying her family and her religion. In this short speech, Jessica is committing two serious sins--rejecting her own father, and, by doing that, rejecting his religion--but, from the perspective of Shakespeare's audience, which believes Jews to be the most serious threat to Christianity, Jessica is making the only possible correct decision--to reject her Jewish-ness (in the form of her father) and accept Christianity (in the form of Lorenzo).
The "strife" that Jessica refers to in her final speech is most likely the strife within herself--being pulled by her obligations to her father as his child and to her religion, on one hand, and being drawn to Lorenzo and Christianity by her love and heart, on the other hand. For Jessica, only one resolution will end the strife within her--eloping with Lorenzo.
The main theme that is dealt with in this short scene is that of duty and identity. Jessica finds herself fighting a conflict that is reflected in the phrase "heinous sin" that is asked about in this question. What Jessica is contemplating is of course eloping with her Christian lover, Lorenzo, which would be a "heinous sin" in a number of different ways: she is showing dishonour to her father through her feeling ashamed of him, she is contemplating abandoning her religion and converting to Christianity in order to marry Lorenzo, and she is going to marry against her father's wishes. This is of course what is reflected in her words in the soliloquy that she delivers in this scene:
Alack, what heinous sin is it in me
To be ashamed to be my father's child!
Jessica is therefore struggling with herself massively as she delivers these lines. Her own duty as a daughter and what she has been taught about the honour and respect she owes to her father comes into conflict with her own desires and natural feelings. What she feels she naturally wants to do is contrasted by what she feels she ought to do, and she has to come to terms with the expectations that are placed on her as the daughter of a Jew. Note the way that Jessica, in the rhyming couplet that ends this scene, refers to "this strife" that she hopes to end by marrying Lorenzo and converting to Christianity. Jessica's decision is a massive one, as she is talking about turning her back on her entire culture, upbringing, and family.