I was recently asked to resign or be terminated by my employer. When I was in my exit interview, I was told I would receive only 2 weeks severance pay. Two years ago, another employee with the same job as me was asked to resign or be terminated was given 2 month severance pay.

Is there any way that I can use the other employee's severance package as a precedent and sue the company for more?

Sorry but they don't even have to offer you two weeks of serverance so a lawsuit to try and get two months isn't going to get you anything but lots of legal fees, assuming you can even find a lawyer to try.

The fact that several years ago they offered someone else something different is irrelevant. You can ask for more, but if they are trying to terminate you, I woudn't bank on it.

It's possible the other employee was with the co. longer than you or there was some some other reason why they were given more severance pay than you. However, it doesn't really matter what they did two years ago since severance pay isn't even required unless you have a CBA or employment contract which guarantees it.