Creating Lower Third mogrt with Sliding Text

You will need some expressions that use sourceRecAtTime() and either scale the text or create a text box that gives you multiple lines. You could also start out with Paragraph Text and let the lines wrap automatically. The proper and efficient approach depends entirely on your design goals.

Take a couple of minutes to take a screenshot of your UI showing all the layers and drag it to the reply field on the forum instead of using the "Drag & drop here..." button so we can see it without downloading it. Then, describe your design goal in detail, and I'll be glad to provide you with the workflow that will work for you. I do this kind of thing all the time.

Maybe something like this would work for the move:

//set up the timing of the move
t = time - inPoint;//start move
t2 = time - outPoint; // start of move out
firstMove = framesToTime(20);//length of first move in frames
secondMove = - framesToTime(10);// length of last move in frames

// Find length of text and set start and end positions
box = sourceRectAtTime();
boxWidth = box.width + box.left; // find width of the text
topEdge = box.top; // find top of the text
strtPos = [-boxWidth, value[1]];
restPos = value;
endPos = [value[0], thisComp.height - topEdge];
// moves
if(t < firstMove)
	easeIn(t, 0, firstMove, strtPos, restPos);
else
	easeOut(t2, 0, secondMove, restPos, endPos);

 If you create a text box, it looks something like this: