While you are actively working in L2L, you will not be logged out of your session due to inactivity. Even if you lock your computer for security reasons, your L2L session will still be active for up to 24 hours.
The exception to this is when you have not been actively working in L2L. Under those circumstances, you will be logged out of your session after 24 hours of inactivity.
For security reasons, it is not prudent to leave your session open and accessible to passersby, especially if you have an Administrator account. Working with multiple windows open in L2L with no activity for extended periods of time (8 hours or longer), can also result in unintended consequences. If you are an Admin viewing Dispatch as another user in one window/session while working under your login in additional windows, excessive periods of inactivity will almost certainly lead to unintended mistakes.
The best rule of thumb is to always lock your computer when you are not physically present and when sensitive data is visible. Adopt the best practice of regularly. logging out of L2L entirely, not just x'ing out of the window. You should also regularly completely shut down and restart your computer. This is a good habit to adopt, for reasons of installing important updates and clearing browser caches.