After Effects :: Text Scrolling In Chat Window?

For my project I created a chat window where the spoken text and questions are written down.

The  window is limited to 3 lines, and each character and line is written itself, using the opacity text animation and its offset value. (like typewriting) how can I drop the first line when a new one starts and push the remaining 2 lines up? The only solution that i thought about is moving the whole textlayer in a mask upwards, but i think there is a much easier solution around.