First off I used google academic to find papers about LastPass, password managers and memory forensics. It was the last one I found to be more helpful
Amari, K. (2009) Techniques and Tools for Recovering and Analysing Data from Volatile Memory.
After gaining an understanding memory extracting and analysis I created a windows 7 virtual machine with 2 GB of RAM, installed some browsers made a few accounts on various websites, installed LastPass, restarted the machine and captured a memory dump using DUMPIT (Search DUMP IT Memory dump). I analyzed the memory dump using SIFT Workstation, in the terminal I used the command
strings windows7.raw | grep “password” > output.txt
Swapping "password" for email addresses, known passwords of the fake accounts, website names etc.. I found nothing, so the memory was clean.
I then logged into LastPass and took another memory dump using the same tool. Analyzing this file highlighted a bunch of hashed values, which confirmed what LastPass says on its site - LastPass stores encrypted hash values in memory.
Next I decided to log into websites and accounts but not all of them just a random number of them and took another memory dump. Using the same methods as before I found decrypted passwords, email address and other information this means that when you visit a website that LastPass has a password for, it decrypt's it and stores in the memory for your browser to use.
I should also state that even if you don’t use LastPass and instead use a browser(s) built in password managers you will get the same results.
So you might say that I needed to know the password in the first place, I didn’t as simply searching for “pass” or in the case of google websites “Passwd” in the memory dump gave the passwords.
If I do this again I would do all the same steps above however, I would log out the windows account and into another account to see if I can get the the passwords from that memory dump, I suspect you would meaning you can log into a public computer and obtain the previous users passwords from there memory dump.
I would say that LastPass is secure until you log into a website, its very unlikely anyone will be able to decrypted the hashed values. In the end don't use LastPass or any other password on a public computer.