I have the same issue

SEE THE FIREFOX BLOG FOR DETAILS ON THE ERROR THAT'S PRODUCING THIS PROBLEM:
https://blog.mozilla.org/addons/2019/05/04/update-regarding-add-ons-in-firefox/

This review is 5-star because there isn't a problem with the extension. The current widespread problems have been caused by the actions of Firefox developers.

NOTE: I found a fix for this Firefox problem!!!!

Original message:

I am yet another person whose Lastpass addon for Firefox stopped working on May 4, 2019. It has been removed from add-ons. When I try "+ Add To Firefox" again, I get the message "Download failed, check your connection".

Also, if I download lastpass_password_manager-4.27.2.10-fx.xpi and try to manually install it, Firefox says that the xpi file is "corrupt".

I am on my way to the lastpass site to also report this to them.

UPDATE: I found a fix. See this post within the LastPass forum! ...

https://forums.lastpass.com/viewtopic.php?f=14&t=331365#p1110235

Firefox has already released a fix for this. It affected many add-ons, not just LastPass. Just go into "Firefox options", select "Privacy & Security", select "Allow Firefox to install and run studies". The update/fix is currently being broadcast this way. Close Firefox, Restart Firefox, give it a couple of minutes and your Add-Ons should reappear. Mine did.