I have already contacted LastPass and their reply was ZERO assistance.

Did you try to clear the Facebook cookies?

You can also try this in a Private Browsing mode window.

Facebook cookies? or Firefox cookies? I have cleared all of Firefox cookies. Does that cover all of the Facebook Cookies as a subset of all Firefox Cookies? This was the advice from LastPass and it was a FAIL.

I am challenged by pronouns. Which "This" is this? Are you suggesting that I try to open FB#1, then close FB#1, then open FB#2 in a Private Browsing mode? No, I have not tried Private Browsing because I have never had any previous experience with Private Browsing, and no one has suggested it before this. Has Private Browsing ever successfully solved a similar issue in the past? And let us say for the sake of argument that Private Browsing would solve this issue for me, would this indicate that Facebook, Firefox, and LastPass would then have enough information to resolve this issue? Or would this then be the only available workaround? I have never read anywhere that using Facebook with multiple accounts would require Private Browsing to be functional.

Private Browsing mode uses a separate cookie jar, so there can't be interference from cookies in a regular session.

I assume that you do log out from account #1 before trying to login to account #2?

Yes, as mentioned in the original post, I log out of Facebook #1 before I log in to Facebook #2. I used the word "Closing" to describe logging out of FB#1.

Does this only happen if you use LastPass or also if you login manually and enter name and password yourself?

Are you using any cookie related extensions?

When I navigate to Facebook.com in Firefox, the system logs me in to Facebook account #1 without any manual intervention. It uses the first of the two user names and passwords in my LastPast Vault. When I log out of facebook, the FB screen I arrive at has the name and password fields populated with my account name and password information from FB#2. (once, but not the next time) I hit enter and it works. I am unsure how logging out of FB sets these fields with FB#2 data only once but not later times that I try it. When I overwrite the two fields, the proper account is logged in based on my manual entry. Usually, the account data that is populated in the Name and Password fields are from the first of the two accounts listed in LastPass. But "usually" is not "always". When I try to use the LastPass Dropdown tool in the right side of the field I get inconsistent results in the password field causing an error. My sense is that it is taking more than a few seconds to populate. No other website login where I have multiple accounts takes more than a fraction of a second to populate correctly and I hit enter and they work. Facebook is the only one with issues.

I have changed both Facebook passwords and the system has stabilized to the point that it is working when using only one method of entry. The "Recent Logins" tool that FB provides with profile photos is non-functional. It will not populate with any data. But I never used it in the past and I do not really need it.

And now the final answer. When I log out of Facebook, LastPass is able to properly log in to the account that I choose in LastPass. But simply closing the Firefox browser window does not log me out and any choice I make in LastPass brings me back into Facebook in the last account I was in. Is this normal for a browser window to not let go of the login?

Quote: But simply closing the Firefox browser window does not log me out

That is why I asked above whether you did log out what you apparently didn't do. If you close the window then you still have the login cookie that authenticates you to the Facebook server as still being logged in and thus this is expected behavior. You always need to logout to clear the session ID on the server an prevent possible misuse of your session ID.

And why am I able to use every other site with no issues like this? When I close any one of my other websites, I can log in as another user with ease. There are still parts of this issue that are not working anything like all my other sites. I find it a challenge to think all other sites are flawed and FB is doing things in the only correct way. I am far more suspicious of FB than most other sites. How does FB and the browser know which of the accounts wishes to log into FB when I log in for the fist time? I am not offered a choice. It decides for me. That alone sounds flawed as though it is remembering things and applying inconsistent rules for what it remembers and when.

This is not really an answer to your questions but a possible solution although I'm not sure it will work with LastPass. When you log out of a FB account you should see a page showing your profile avatar with the option to add another account. Add the other account. When you next want to sign into FB it will allow you to choose which account and as you log out you it will take you back to the same page to allow you to log into any other account. Only problem is you will now have told FB which accounts are associated with you.