My MBP2011 now has the same issue.
I use it for work including doing graphical work and websites and now the machine is pretty near useless to me as any time I try to use Photoshop or do anything graphics heavy it does the white lines thing. I have found out (among other things) that this is more than likely down to faulty soldering of the GPU on the logic board.
It's out of warranty and I don't have Apple Care but if I did it would have run out by now. So I am in the position of scrapping the machine or replacing the logic board which 1) costs a fair bit and 2) may not even solve the issue.
As I bought the machine direct from Apple and not through a reseller, I have been in touch with Apple Executive Relations and they have offered me a gesture of goodwill to fix the issue and cover the cost. I think I am one of the lucky few to have been offered this but I did find out a few things whilst on the phone with them and in my research of this issue. I thought I would share them with you.
1. There are three threads on the Apple forums that I could find that now have over 2 million views and 10,605 (at time of writing) replies - mine will make 10,606 I guess.
2. I was told that if you experience this, or any other technical, issue you have to follow their process which is: go to an apple store to get the machine looked at, get it repaired. Simple, but they will only cover the cost of the repair if you are under warranty or in the 3 year period of your apple care. However, in the UK you can claim against the reseller for defects like this under UK consumer law for up to 6 years after purchase. I suspect this may be easier than it sounds.
3. They wouldn't tell many how many complaints about this issue they had received, but they did say they were investigating the options but there was no decision from Apple yet. Reading between the lines this says to me that they know there is a problem (if there wasn't what would they be investigating???) but don't know what to do about it or don't want to do anything about it. But that's just my supposition.
4. I was also told that it was difficult to speak the issue I was experiencing generally (because I brought up the fact that so many other people seemed to be having the same issue) and that even if the symptoms looked the same it might be a different cause. Hmmm.......
5. I was also told (because I was sceptical of the logic board fix being offered to me) that this resolved the issue in the majority of cases. Again that makes me think they have received a fair few (and when I say that I actually mean a LOT) of complaints about this issues.
6. Lastly, there is an online petition about this issue which has now passed the 10,000 mark. I asked the man from Apple at what number would they consider this a critical issue and initiate a replacement programme like they did with the 27-inch 2011/2012 iMacs that had a video card problem? He said he couldn't comment on that.
My advice for what it is worth is - post your experience here, sign the online petition (just search for MBP 2011 petition on Google and you'll find it - I am not sure if I can put the actual link up here), and then get in touch with Apple Executive Relations and see what they say to you.
Finally, I saw a great quote from ttrtilley on one of the many forums that has a thread about this issue, which was "Too many lemons from Apple". It's quite apt given the global and highly widespread nature of this issue.
I do feel given to what I have read about this online that Apple's reputation is being damaged on a large scale and what I find bemusing is their apparent attitude to it. No decision has been made yet? Well I wouldn't waste any more time thinking about it - they just need to sort it out or they will start to lose more than "face".