I'm sure there's a way to get a text animator to do this, but the simplest way I could figure out was to use a track matte and then move the text down to reveal a line at a time. You'll want to reverse your text by putting an expression on its Source Text (or reversing the lines in a text editor):
text.sourceText.split('\r').reverse().join('\r');
And then you could put an expression on the text's Y position (right-click Position, Separate Dimensions) to move it down a line per, let's say, second:
transform.yPosition += Math.floor(time) * 36; // replace 36 with your leading
Hope that helps.
