The phrase "natural lord and king" (or just "natural lord") refers to the king. There are various examples of this:
texts about and by King Charles II:
... That we do not represent this day the Person of a Tyrant or Usurper as some of late have done, but the Per∣son of our natural Lord and King, Charles the second, by the Grace of God of England, Scotland, France and Ireland King ...
From a speech by the Lord Chancellor of Ireland
... as you ought to doe to your true and natural lord and king ...
From a translation of a letter from King Charles II excerpted from The third part of the History of the Reformation of the Church of England
By Gilbert Burnet
About King Harold:
And, ultimately, nothing can alter his status as a natural lord:
Harold is a legitimate king.
From Royal Responsibility in Anglo-Norman Historical Writing by Emily A. Winkler
The Black Arrow by R. L. Stevenson:
“No natural lord of mine,” said the man in the smock. “I followed the
Walsinghams; so we all did down Brierly way, till two years ago, come
Candlemas. And now I must side with Brackley! It was the law that did
it; call ye that natural? But now, what with Sir Daniel and what with
Sir Oliver—that knows more of law than honesty—I have no natural lord
but poor King Harry the Sixt, God bless him!—the poor innocent that
cannot tell his right hand from his left.”
... as a false traitor against the most illustrious and excellent
prince James the second, by the Grace of God of England, Scotland,
France and Ireland, king, and his natural lord ...
A Complete Collection of State Trials and Proceedings for High Treason
By Thomas Bayly Howell
The "natural" aspect, as far as I can tell, arises from the principle of divine right - the king is the king by grace of God, and as such, is naturally the subject's lord (unlike other positions in the nobility, which are usually positions created by human law and not God's natural law).
From the context, I do not think the monster is calling Frankenstein his natural lord and king, but is instead talking about the country's king. Note how this conversation starts with Frankenstein berating the monster for the murders he committed:
“Devil,” I exclaimed, “do you dare approach me? And do not you fear
the fierce vengeance of my arm wreaked on your miserable head? Begone,
vile insect! Or rather, stay, that I may trample you to dust! And, oh!
That I could, with the extinction of your miserable existence, restore
those victims whom you have so diabolically murdered!”
And in the monster's response to that:
... How dare you sport thus with life? Do your duty towards me, and I
will do mine towards you and the rest of mankind. If you will comply
with my conditions, I will leave them and you at peace; but if you
refuse, I will glut the maw of death, until it be satiated with the
blood of your remaining friends.
From these lines, it seems to me that the monster is saying he will not further violate the king's law - provided Frankenstein fulfills his responsibilities.