This is more of a warning than a solution. Many have commented this.. but it seems worth having as a solution.
Once you've started making any progress on this --
DO NOT DOWNLOAD ANY UPDATES!
I was at about 75,000, the latest update reset all of my progress once again.
As for the best way to get tons of lines, look for the speed tournaments. In particular the ones with constant blitz.
I use the time bonus, avalanche and blitzn - on the speed tournaments I average around 260 lines. For a regular game it's about 150.