You can manage various security options within your LastPass preferences.

• Log out when all browsers are closed – Specify when LastPass should log out of your session upon closing all web browsers that are in session with LastPass. Check the box to enable this feature, and when you relaunch a web browser, you will be asked to enter your master password. If you want to stay logged in to LastPass upon browser close, leave the box unchecked. This setting is disabled by default.
• Log out after this many minutes of inactivity – Specify the maximum amount of idle time (no keyboard and mouse activity on the machine at all, not just no activity on the browser where the extension is installed) that you want to have pass before LastPass automatically logs your account out of the active session for the web browser where the extension is installed. After the specified amount of time (in minutes), an inactive LastPass icon is displayed to indicate that you have been logged out. Please note that if any activity on the machine occurs before the specified logout time, the countdown to logout time will be reset. If you want to remain logged in to your LastPass account via the LastPass browser extension regardless of idle time, leave this setting unchecked. This setting is disabled by default.
• Require master password reprompt – If you want to protect a particular Site, Secure Note, or Form Fill Profile so that any access using the information stored in LastPass requires your master password, you can check the box to enable this option while accessing the Edit window for the entry. This provides very specified control of individual sites, such as a bank login, where you may want additional security. Please note reprompt is not as strong as logging off, we recommend utilizing the above logoff options to fully protect your data. Learn more.
• Clear Clipboard after use – LastPass is set to clear your clipboard after a default amount of time. If you’ve been copy/pasting your secure data into login fields or web forms, this ensures that your data cannot be compromised by being left on the clipboard. You must have the binary component installed for this option.