In Parashara, the lord of a house is the lord regardless of whether any planet tenants it. In KP, if no planet occupies a house, the reading becomes dependent on the other levels (cuspal sub-lord, planets aspecting, house lord).
But there is a subtlety: If you are analyzing when the 2nd house (wealth) will bring results, and Mercury (business planet) is the 2nd house lord but NO planet occupies any of Mercury's ruled stars (Ashwini, Jyeshtha, Revati—the three nakshatras Mercury lords), then Mercury is "untenanted" and its promise is weakened or unfulfilled.
Untenanted planet rule: If a planet's stars have no planet tenanted in them, the planet's signification is delayed, weak, or absent. This is especially critical in horary (Prashna) astrology, where an untenanted planet often means the answer is "No."
Application: A client asks "Will I get this job?" Look at the 10th house (career). If the 10th cuspal sub-lord is Saturn, but Saturn's stars (Pushya, Anuradha, Uttara Ashadha) have no planets in them, Saturn is untenanted. The prediction becomes: "Job is not immediate; Saturn's timing is blocked."
Rahu and Ketu: These shadowy planets complicate the untenanted rule. Rahu acts as an agent for the planet whose sign it occupies. Ketu acts as an agent for the planet whose sign it occupies. An untenanted Rahu or Ketu requires examining which planet's signification they are masking.
The calculator identifies untenanted planets and flags them in the significator report. You will learn to recognize when a promise (job, marriage, health) is blocked by an untenanted significator and advise the client accordingly (e.g., "The promise is there, but timing is constrained").