Greetings!
Hmmm...well, I suppose one could look at what one's religion--or one's interpretations of the doctrines and commandments of their religion--as some inspiration for their actions.
If one supposes that there really is a spiritual realm, and that people who are swayed, influenced, and/or possessed by evil demonic spirits, and that their heretical attitudes and actions can, *in fact* have an evil influence on other people, whom you are trying to save from such evil, then it could be argued that executing such people is the highest good. Doing so through the order and discipline of the law would be Lawful, so perhaps there could be the argument for Torquemada being "Lawful Good".
Indeed, it is popular to assume that Lawful Good people must be compassionate and merciful, but that isn't what is in the Player's Handbook--where it says that "Alhandra, a Paladin, fights against evil, showing no mercy."
There is a spiritual warfare paradigm that Torquemada is operating under. Demons really *do* exist, and work their evil through human beings on a daily basis. In some ways, it can be seen as being a type of cancer, that spreads throughout the community. There are examples in the Old Testament where it is decreed that all of one's enemies--be they men, women, children, even their animals and other livestock--are to be slain, because God chose to punish whatever evil nation for their evil and wickedness, and because God did not want the Jews to be contaminated physically and spiritually by the people of the evil nations.
In a similar fashion, it is these kinds of ideas that seem to have inspired Torquemada, and may have been an aspect of their interpretation of the particular Scriptures and the doctrines contained therein. There are so many different paradigms and underlying assumptions about spirituality and reality that can be considered. If one assumes that the paradigm that Torquemada was operating under, then he would be Lawful Good, because the spiritual purity of the community, the defeat of evil, and the absolute obedience to God is seen as the highest good. All other considerations are of far less importance than these things. One must remember, people of the 15th century did not share the same world view that modern people of a democracy do. In fact, under the concept of the "Divine Right of Kings"--that is, the King is annointed and raised up by God Himself to rule a nation, defend the faith, and defeat evil. By such, "Democracy" could be seen as a form of political and spiritual rebellion. Torture, for example, was seen as something that was good. In general, throughout various nations at the time, many who were accused of various crimes, it was considered that they were guilty, unless *proven* innocent. That is an entirely different paradigm than what is held in America, for example. Still, if one desired to look at many different details, there are many things that nearly everyone in the 15th century considered to be just and good, that we today would consider horribly evil. Likewise, there is a great deal of things and ideas that we, today, consider just, tolerant, right, and good, that those of the 15th century--from the lowest peasant to the highest noble--would consider abominably evil and wicked. The contrast in world views really is stark and hugely different, even greatly in opposition.
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Well, at least that is how in some ways such a paradigm could have been embraced by Torquemada, among others.
I would say that in alignment, Torquemada is probably Lawful Neutral, and from his training and position, I would say he would be a Cleric, rather than a Paladin.
Semper Fidelis,
SHARK