In the first sentence, it means in addition. In the second sentence, it means in control of the situation.

Bean, in both of those examples you provided, it actually has different meanings. When you used it in the sentence "On top of it, I lied to get in, so basically I'm a shallow loser." It means besides doing whatever else they did, they a also lied. They did something and "on top of that" they also lied. I hope I am being clear with my explanation. The second example, "I'm just making sure you were on top of it. I'm on top of it." With this usage someone is saying they want to make sure you are taking care of something or you are doing something that needs done. For example. John: "Hurry up and clean the house! Your mom will be home any minute!" Jimmy: "I'm on top of it!" I hope this was helpful.