First, for assessing suicidality, remember SLAP:
S - Suicidal ideation
L - Lethality
A - Accessibility
P - Plan
Unfortunately, they couldn't put it in the actual sequence of assessment (well I supposed they could, but "slap" sounds better than "spla" (or God forbid, "splat"). Basically, when it comes to suicide, you first want to know if they have thoughts about it (and no, asking if someone is thinking about suicide does NOT plan the idea - they've done plenty of research to disprove this myth!) - Suicidal ideation. If they do have thoughts, you want to know if they have a Plan. If they have a plan, you want to know if the means are Accessible, and how readily (something that's in the house? something they know where to buy?). Then you want to consider its Lethality (i.e., likeliness they could survive if they act on it).
However, it's probably more important to consider intent - not part of the acronym, but for my money, more crucial than lethality. After all, if someone has a lethal plan they'd never act on, they are at less risk than someone with an ostensibly less lethal plan they have every intention to act on. Plenty of people die by "less" lethal means, sometimes even when they only intended the act as a so-called "cry for help." It's Russian roulette.
The second mnemonic has to do with people's motivation for attempting/committing suicide. These factors help us recognize serious suicidality, and better understand our suicidal clients. They are the 3 R's:
Relief is perhaps the most obvious. People who think about suicide are typically in pain - mental, physical, or both. They may have lost hope of ever feeling better while living, so they begin to consider whether they might be "better off dead." Even people who think there is no form of existence after death may think that at least their pain will end. If it starts to seem worth it - that's a big sign of risk.
Many people do believe in some form of existence after death, however. Therefore, they may not only think their current pain will end, but also think that they will get a better life instead - i.e., Rebirth. That includes both reincarnation (rebirth into a body on this earth), and "rebirth" as transition into some other form of existence (e.g., heaven). An idealized image of a better life can be a powerful motivation for suicide. Even more powerful, perhaps, can be an image of Reunification - getting to see and be with loved ones, both people and pets, that have died. This motivation is a major reason why recent loss is a risk factor for suicide.
Finally, sometimes the motivation for suicide can be less about oneself, and more about someone else. Sometimes people develop a fantasy about how other people will feel and react if they die, most notably loved ones. Suicide can seem like the ultimate way of getting the "last laugh" - causing pain without the possibility of retaliation.
While none of these things are...pleasant...to think about, they are all important, because most of us work with clients who already have risk factors for suicide. What other things do you keep in mind when you think about suicidality?