1) Using LastPAss doesn't mean one stores sensitive passwords in it. You can memorize a few that really matter (email, bank, etc) and keep the rest there.

2) They claim it's secure:

    This is important because your sensitive data is always
    encrypted and decrypted locally on your computer before
    being synchronized. Your master password never leaves
    your computer and your key never leaves your computer.
    No one at LastPass (or anywhere else) can decrypt your
    data without you giving up your password (we will never
    ask you for it).