Many Notorious Monsters (and some ordinary monsters) appear via Lottery Spawn. This means that when a Spawn Point for an enemy is about to be filled, there is a random chance (as if drawn from a lottery, hence the term) that an NM may spawn instead. For example, the Damselflies in Valkurm Dunes above Whitebone Sands have a chance to spawn the Valkurm Emperor.
The enemy (or multiple enemies) who may spawn the NM is called a "Placeholder." Killing the Placeholder frees up the Spawn Point, allowing the "Lottery" to determine whether either the Placeholder will spawn again, or the NM. This is critical difference between lottery spawns and other spawns, if the placeholder for a lottery spawn is not killed then the NM will never appear, but for a non-lottery spawn the monster will eventually appear whether other monsters are killed or not. Placeholders are usually, but not always, the same type of monster as the NM.
When the NM is defeated, there is usually a certain amount of time before it can be placed back in the "Lottery" to spawn again; this is the NM's "Respawn Time," even though the variability of the "Lottery" will ensure the NM will not necessarily reappear after that specific amount of time. Respawn Times in this instance, then, tend to refer to the minimum time before the NM respawns. This also means that they are almost always of a range more variable than Timed Spawns. For example, the aforementioned Valkurm Emperor has a Respawn Time of 60 to 90 minutes; Leaping Lizzy is said to have a Respawn Time anywhere from thirty minutes to six hours!
In Lottery Spawn situations, if an NM hunter knows the Respawn Time of the hunted NM and learns its Time of Death, he or she will be placed at an advantage over hunters who do not. Coupled with knowledge of the NM's Spawn Points, the hunter will know both when to begin checking, and where to check for Placeholders. Learning these facts and applying them serves as the basis of hunting Lottery Spawned Notorious Monsters.
Note that probabilities of NMs actually reappearing are different in almost every instance—Respawn Time only serves as a rough "guideline" for hunting, and is not an exact science by any means. Some NMs will always spawn within a few minutes of the respawn timer (Stroper Chyme); some take hours or even days to spawn (Valkurm Emperor); still others are only allowed to spawn during certain weather conditions (Geyser Lizard) or times of day (Spook), adding other factors to the hunt. NMs that are hunted more often are also more likely to have their probabilities changed from update to update, to prevent monopolization of the NM's items. The more an NM hunter knows about the NM, the more prepared that hunter will be.
There are, however, some people who have theories as to how to spawn an NM faster than normal. For example when camping Leaping Lizzy; using Widescan, looking for the fifth lizard in the first group of five and only killing that one single lizard over and over again has been reported to reduce spawning time dramatically. It's been reported that up to three spawns in around twenty minutes has actually occurred. This theory also suggests that every "fake" placeholder that is killed, it increases the NM's spawn time by a certain number of minutes, presumably five. It has been reported that similar strategies have been found for other Lottery NMs such as Valkurm Emperor, Jaggedy-Eared Jack, and Fungus Beetle. This may also account for why some NMs can take days to appear.