I recently visited a historic Buddhist temple in Japan and a grave there was in honor of the wife of a feudal samurai lord. The woman was referred to as the lord's "lady" in English. Is it an appropriate expression? I thought a "lady" could also mean a lover.
As pointed out by others, the in European custom historically used by the nobility, a "Lady" is a noble woman, typically the wife or daughter of a Lord. Similar to a Queen, Princess, Duchess, or Baroness for women related to a King, Duke, or Baron. So the use of the term (title) "Lady" for a noblewoman is correct English but it may not translate directly to use in Japan (today or historically). It's a sign of respect or status, similar to how the Japanese use "Sama" rather than "San" for individuals in particular positions.
Generally women in non-marital relationships with a Lord (for love or lust) were given other terms such as "mistress", "concubine", or "courtesan". In the West these terms have fallen out of use because of their connotation with infidelity and the decline of political or arranged marriages. Whether these other women held any influence or status depends on the time and culture. Some societies respected these extra-marital women as the Lord's chosen inner circle, others viewed them as little better than prostitutes (they were literally sleeping their way into the highest tiers of society).
Whether she was the "Lord's lady" is more complicated and depends on whether she held power of her own (e.g., ruling in his absence) or was seen as belonging to the Lord without power or respect on her own. In English-speaking countries, women are no longer viewed as property or marriages as political transactions so this usage is uncommon and sounds strange today, though it may be accurate in a historical or fictitious context. Whether the Lord's wife gained more respect as a leader herself would be difficult to tell, given how polite and respectful the Japanese are to everyone.
I would venture that it will be difficult to say exactly what is correct. Any number of cultural influences may affect the meaning - "historic", "Buddhist", and "Japanese" may all impact the correctness of a translation. In fact, their may be no exact translation at all.
In European culture (as mentioned) Lord and Lady were a married couple, but do these same rules apply in feudal society? Also, do not neglect to consider how the use of more common terms like Mr., Mrs., and Ms. have evolved in usage. The abbreviation pronounced Mister was originally short for Master and Mrs. is an abbreviation of mistress, not missus. The common usage of "mistress" has changed and would not be an appropriate introduction today.
Perhaps the most correct translation today might be "Ms."