In Henry James' novel, The Portrait of a Lady, the quote, "We can do absolutely as we please; to whom under the sun do we owe anything?" refers to Caspar's plea that Isabel leave her husband, divorce him, and start a new life with Casper because Caspar is still in love with Isabel. In light of Osmond's treatment of Isabel and his behavior, Caspar believes she has the right to do so.
However, in reference to the title of the book, Isabel sees herself as a "lady," with responsibilities to fulfill. Although Osmond and Madame Merle have conspired to get Isabel to marry Osmond so she can support him and their illegitimate child Pansy, Isabel does not believe she can afford, as a lady, to act without grace or respectability.
And, in all of this, Isabel is very fond of Pansy, and has vowed never to leave her. So Isabel turns her back on Caspar's wishes, and without informing him, returns to Rome to her marriage, even though it is a sham, to do what a lady would do, and to see to the well-being of Pansy.
It is at the very end of the novel when Caspar Goodwood--the persistent suitor whose love for Isabel Archer remains undiminished throughout the entire novel and Isabel's marriage with Gilbert Osmond--utters these words to Isabel as part of his attempt to convince her to divorce her husband and run away with him. Isabel Archer has defied her husband who mistreats her by disobeying his express orders not to leave him in Italy. She, regardless, left to go back to England to see her cousin Ralph one more time before he died. Caspar Goodwood sees this as a sign of her desire to leave her husband and her unhappy marriage and start a new life:
"You took the great step in coming away; the next is nothing; it's the natural one. I swear, as I stand here, that a woman deliberately made to suffer is justified in anything in life--in going down into the streets if that will help her! I know ho you suffer, and that's why I'm here. We can do absolutely as we please; to whom under the sun do we owe anything? What is it that holds us, what is it that has the smallest right to interfere in such a question as this?"
However, Isabel Archer turns away from this insistence precisely because she feels that the bond of marriage means she cannot do absolutely as she pleases and she does owe something to somebody. Thus it is that she makes her momentous decision to pass up this opportunity for happiness and return to a loveless marriage in Rome.