How do I convince others of the importance of password management?

Your wife is not using LastPass because she has better things to do, not because she's incapable of realising its utility.

You would think that once people properly understand the risks they're exposed to (which requires a serious amount of education), they would automatically start to comply with whatever security advice is thrown their way. Well, this assumption has been proven wrong multiple times. See Herley's 'So long and no thanks for the externalities', which has a couple of examples of wasteful security, and Beautement and Sasse's 'Compliance Budget' for a general theory of how humans behave with regard to security.

In economics of information security, there are several examples of people willingly taking risks because it saves time they need for other tasks, or because they perceive potentially negative side-effects to complying (such as being locked out, or embarrassed in front of someone else).

Hence, rather than insisting on your wife doing what you think is good for her, identify her needs, her priorities, her worries and her actual problems. Then, deploy a tool that does work for her (if there's any) and work with her to make sure she knows how to use it and perceives its utility and limitations properly.

For instance, I don't use password managers because I use some of my accounts on so many devices that I have to know the passwords, because I have some passwords that have to comply to such silly policies and be changed every other day (and I hate having to resync my passwords on each device), I don't trust online password stores the least in the world, and because some of my devices are targeted often enough that I don't want them storing many passwords. Most of these problems I have are probably addressable one way or another, but I don't want to lose a day of work setting up processes that go against my habits. And yet, I'm a security engineer. In conclusion, most users will prefer appropriateness and value to security in most decision-making situations.