I dont think you are gonna find anything of use in Lords of men.
As far as I can tell "landed knight" is not actually a game term. I believe that you have gotten the virtues "Knight" and "Landed Noble" mixed together, and coincidentally that combination of virtues is a good guess at how to describe your character.
Lords of men do refer to "landed knights" as a social class, namely knights who hold land. But the books does not ascribe any special rules to being a landed knight, other than to say that the virtues "Knight" and "Landed noble" are an appropriate combination of virtues of people who want to play a character who is a landed knight.
The virtue "Knight" makes it so that the character is a knight, which just means that the character has been knighted by someone, and that confers some social expectations and privileges.
The virtue "Landed noble" means that a character hold the right to land from someone else higher in the system.
Given that the character that you describe is explicitly a knight then I would say that the virtue "Knight" is pretty appropriate.
The royal employee part you could simulate in some different ways, the most obvious is to say that it is about equivalent to holding the land oneself as a "Landed noble", since the character, as far as I can tell, administers the land. For me that would be close enough.
You could also go with some other combination of virtues, you could go for "Wealthy" to simulate that the character has money not normally available to a knight, but "Wealthy" doesnt actually make the character all that much richer, it just means that they have to work less in order to have the same amount of money.
You could decide that the combination of "Temporal influence" and "Protection" are a better fit. "Temporal influence" to simulate the greater power afforded to such a character, and "Protection" since the character can presumably rely on their patron for protection.
I hope this helps you out.