Yes I said women are 3x more likely to attempt, and men 3x more likely to complete. And yes I said this is majorly due to lethality of means. I didn't say anything specifically about guns. Men tend to choose more lethal means which includes guns, hanging, etc., while women choose overdose (often not lethal doses), cutting, etc. Of course this is not black and white, but tendencies. Other factors that are likely not quite as important but still important are what Stannis referred to: capacity for suicide, access to support, willingness to seek support, etc.
In terms of capacity for suicide, I'd encourage anyone interested to research Thomas Joiner's Interpersonal-Psychological Theory of suicide. Historically, suicide research has mostly looked at individual risk factors or groups of risk factors, which results in kind of a checklist so to speak of how many risk factors are present for a person. Helpful, but not a ton. Joiner's theory (which is relatively newer) is more of an actual theory than any others before. He breaks things down into two areas: desire for suicide (which includes perceived burdensomeness and thwarted belongingness - and those two can be broken down further) and capacity for suicide (which can be broken down further).