When Lady Macbeth speaks these lines, she just has read a letter that her husband sent about his meeting with the three witches. He says that the witches told him he would become King. Lady Macbeth knows that he will have to kill Duncan to make this fortune come true. But she is afraid he won’t be ruthless enough to murder him.
Shakespeare often shortens verb forms to fit in the meter or rhythm of his lines. So the lines “What thou wouldst highly, thou wouldst holily” simply means whatever you want to get a lot, “highly,” you still want to get without doing anything wrong, “holily.” The compressed verbs also let him use alliteration with the “h” consonants in highly and holily.
To put it another way, Macbeth is not willing to do whatever it takes to get what he wants. He’s too nice a guy. A few lines earlier Lady Macbeth explains this quality in a famous quotation, Macbeth “is too full of the milk of human kindness.” Lady Macbeth wants him to become king at any cost, even murdering Duncan. She must figure out how to push Macbeth to go against his own instincts and finish the job.
The irony has to do with the roles of man and woman in the play. The man who is supposed to seize the throne, Macbeth, lacks the cruelty to do so, while the woman, who is supposed to nurture life, has the violent will. Shakespeare stresses this irony by using “milk” to describe Macbeth, the man, rather than to describe Lady Macbeth, the woman, with a common phrase like “mother’s milk.”