when I run this against a user mailbox it shows LastLoggedOnUserAccount as different account rather user's account tiself. I have checked that no one has access to thi suser account but it seems somone accessing his accounts. any thoughts on this?

Is the other account a user account ? Certain service accounts have permissions on all mailboxes like Blackberry.

yes this a simple mailbox. I ran the same Get-MailboxStatistics -Identity | fl on my account but it shows me as the LastLoggedOnUser Account. I know there are service accounts who has permissions on it by running Get-Permission.

I figured it out. It was user's calendar which was shared with other team members and those users were shown in the LastLoggedOnUserAccount. Which is kind of weird for me. I would never know If I have not shared my calendar and ran the same cmdlet.