Final answer:
Macbeth is comparing Banquo’s lineage to a 'grown serpent,' which symbolizes a threat to his power as described in Shakespeare's 'The Tragedy of Macbeth.'
Step-by-step explanation:
Macbeth's metaphor of “there the grown serpent lies” refers to Banquo’s lineage. In the context of Shakespeare's The Tragedy of Macbeth, Macbeth considers Banquo’s descendants a threat to his power. Specifically, the metaphor implicates that Banquo’s children represent a danger akin to a “grown serpent” because they are the prophesized heirs to the throne, whereas Macbeth desires to establish his own lineage as the rulers of Scotland.
Macbeth is consumed by the worry that his actions might have secured the throne for the seeds of Banquo's bloodline rather than his own, which is symbolically akin to nurturing a dangerous snake.