Re: Please oh wise ones
First, I must state it is good that you recognize the potential need to back out of Last Pass. You should prepare yourself to potentially have to change every password for every account you have stored in Last Pass. Every one of us should realize we may need to do the same no matter how you manage your passwords. You should start by prioritizing, identify the most important accounts. I have hundreds, maybe thousands of passwords to consider. I have a few dozen I would change immediately and begin storing in an alternative location such as in a paper notebook. Depending on the circumstances I may at that point go into a wait and see approach before I expend substantial effort for lower value accounts.
The current Last Pass situation does have the hallmarks of a dumpster fire in the making. But while the chestnut "where there is smoke there is fire" is often proven true, the extent of the fire is what matters and that can vary enormously. The key is to be vigilant, but act appropriately according to the situation.
"What is local storage?" Local storage for computer systems is where data can be semi-permanently stored without needing to traverse a network|cloud to the storage of another computer somwhere on the network|cloud. It works this way, If the network|cloud (i.e. The Internet) is down, local storage is still accessible and the information stored there.
A philosophical question of sorts; If the network|cloud is down, do you need access to passwords for accounts on the network|cloud?
Local storage to one computer on a network|cloud is network|cloud storage to any other computer on the network|cloud. If you accept that, then you need to realize you must apply appropriate security|protection to any information on any networked computer. Passwords stored locally on a networked computer should be protected as if they are anywhere else on the network. PROPER encryption is a very good way of providing said protection. Sorry for shouting, but improper encryption is an oxymoron.
For proper encryption, Password Safe was presented in previous comments as a good way to do this, I agree because of the original author being Bruce Schneier, a world renowned cryptoghrpher who can also program. I have previously commented on the "pass" program mentioned earlier in the comments. The author of that tool, Jason Donefeld, is a relative newcomer relative to Bruce Schneier, but is building a very good resume in cryptography. There very well may be others, I have not looked into the matter recently. Encryption is heavy math intensive, few programmers can get it right. The best that can, want others to review their work for mistakes of any sort. Yes, even Bruce Schneier wanted feedback on his password safe tool. This is why other commentards have stated that open source password tools are to be preferred over closed source or even worse closed source with proprietary encryption algorithms.
We regular commentards here do get wrapped up in our techiness and become myopic at times. The pragmatic among us often do remind us not to let the perfect be the enemy of the good. By this I mean that browser password managers are good but not perfect. They are accessible to the masses and can do far more good protecting passwords in general being easier to use than many other not quite perfect password managers.
Just remember, if it is too easy, it is probably not too secure. If is is too secure, is is probably not too easy. Find the secure enough middle ground.