This is definitely not true in the UK (where the term “Crown lands” is not used - the equivalent would be “Crown Estate”), and I don’t think it’s true in any of the Commonwealth kingdoms. The Crown Estate is only notionally owned by the monarch. For all practical purposes it’s government-owned land, managed by a public authority, with revenue going to the Treasury. Historically, the civil list, i.e. the annual allowance paid by the government to the royal household (now renamed the “sovereign grant”) was the compensation paid by Parliament to the King in exchange for the King surrendering control over the Crown Estate; but just quantitatively, the annual revenue of the Crown Estate far exceeds the sovereign grant.
By the way, if we’re looking for a case where the distinction between the Crown and a fiefdom subordinate to the Crown still matters legally, the English law of bona vacantia is an interesting case at hand. It governs what will happen to the assets of someone who dies without a will and without any next of kin who could inherit under the rules of intestate succession.
In England, in such cases the estate will normally pass to the Crown, i.e. effectively the government. But for historical reasons, special rules apply to the Duchies of Lancaster and Cornwall. They’re both ancient fiefdoms; Lancaster is held by the monarch himself (i.e. Charles, but as a lien from the Crown, not in his capacity as King; so in effect, Charles is a fief to himself here), Cornwall by the monarch’s oldest son (currently William). In those territories, bona vacantia assets go to the Duchy, and this is actually enforced in practice, although the policy is that the royal family would not personally benefit from the assets but donate them to charity. In legal proceedings in such matters, “the Crown” is replaced by “The King in Right of His Duchy of Lancaster” or by “His Royal Highness the Duke of Cornwall”, respectively.
In case you’re interested, here is some information about this from Farrer & Co, the law firm that has been acting for the royal family for centuries.
But the term “my lord” is simply referring to boss of the territory by the term used at the time.
The OP is asked for the equivalent of the White House.