Most browsers store their passwords in plain-text, this means there's applications that can fetch all your stored passwords from all browsers and send them to an undisclosed location in seconds given user level privileges on the machine.
By upgrading to lastpass you have reduced that attack surface by using a secure passphrase and encrypted data-store but you have increased your attack surface to anything accessing lastpass servers and application bugs.
With all these attack vectors one might think that it's better to just not save passwords and just remember them, while this is true in theory in practice it's impossible to remember a sufficiently unique password for each website you are registered to which leads to password reuse which is another much greater attack vector where your leaked passwords from one site can be reused on other sites.
In general I would advice you to use a password manager that generates and encrypts passwords (Lastpass is one of them), use a secure passphrase and don't reuse passwords. Password reuse will likely make you less secure than writing your passwords on a post-it by your computer (don't do that either)
I would also consider looking into using proper 2-factor authentication for sensitive login (document storage, email, password manager) but I don't want to bore people with the details there so I'll defer you to do some independent research
TLDR
* Store passwords encrypted (Lastpass is fine)
* Don't reuse passwords on different sites