Here is an idea.
I made the first line wiggle between mid of comp and 0. Then, for each of the following, I made them wiggle from the previous line to the end of the comp. Make sure to set the x positions of the lines to 0, otherwise you will have to subtract it from the wiggle and that is just unnecessary computing.
On the first line put this expression(after you set the first value of position to 0):
startPos = thisComp.width/4;
freq = 1;
wiggDistance = startPos;
[startPos+wiggle(freq,wiggDistance)[0],value[1]]
Duplicate it and then, on the second line put this expression:
prevPos = thisComp.layer(index+1).position[0];
wiggDistance = (thisComp.width-prevPos)/2;
startPos = prevPos+wiggDistance;
freq = 1;
[startPos+wiggle(freq,wiggDistance)[0],value[1]]
Now, you can duplicate this second line for as many times as you want. You may want to diminish the wiggDistance for the first line if you add a lot of line, because the left part of the comp will have less action.