I am confused at your explanation-in the beginning of the paragraph, you say she attempted delivery at the time she was at your box. This means the package had to have had a barcode on it for her to scan, because that is how it records the time and action taken (such as delivery). You go on to say that when you got the package today, there was no mail confirmation on the package (then there would be no barcode for her). Are you talking about the same package-is it possible you have a package still awaiting signature (for any number of reasons) at the PO?
You keep saying the carrier is 'lazy' and 'lying' which is a pretty heavy accusation. It really is much easier to just deliver the packages than to load them all up in the morning, then unload them in the evening . Of course, it's also possible an error was made, especially in this very busy time of year. It seems so harsh for the carrier to be judged as a liar for what could have been a mistake.
I had a customer call my supervisor and swear up and down that she was home 'all day' awaiting delivery of her package and I 'hadn't even tried'. I
had gone to the door and rang AND knocked-I knew she was usually home and suprised she didn't answer. After she called and I brought her back the package, she looked at the time deliver was attempted and admitted she had taken a shower at that time...

I wasn't overly offended because she was older, but yeah, people do call over things that could possibly be their fault.