Golconda according to White Wolf canon
White Wolf's Vampire the Masquerade talks about Golconda: a mystical state of enlightenment where a vampire is no longer subject to the Beast, or alternatively the Beast and human aspects of a vampire are in balance.
How Golconda is achieved is somewhat vague, however a rough outline of events has been developed in the Vampire supplements (notably Chaining the Beast).
To start a quest for Golconda, a character must find out about Golconda, as the topic is not that commonly discussed in the Camarilla (and not discussed by the Sabbat). Golconda lore is rare, and like most things, can be used to trap an unwary vampire. Inconnu are generally assumed to be the experts on Golconda (as they're assumed to be just about everything else), but Inconnu are notoriously hard to find. From this point on, the character presumably has a guru to guide him.
Following this, the vampire must regain Humanity and feel remorse. Mechanically, this is expressed by keeping Humanity above 7 and by spending Willpower to avoid frenzy under all circumstances. During this time, the vampire makes amends for his crimes as extensively as he can. Canonically, a character cannot achieve or stay in Golconda unless his humanity remains at at least 7, and Paths of Enlightenment don't count.
At this point, the character is guided through a suspire, which is a vision quest of some kind where the character deals with his state as a vampire. The suspire is a test, which the character may fail. If the character passes his suspire, then he achieves Golconda. If he fails, he will never achieve Golconda. Characters who fail their suspire are likely to wassail.
What's different at LAmush
Although LAmush does not use the Humanity-trait, the term 'Golconda' does turn up in our lores. But if it exists and if so, how it can be achieved? Is a mystery for you to find out.