I think when you've followed Lana for a while you realise one of the fun things about her is literally anything can happen. I would keep your eyes on the various bits of web news out there over the next few weeks and just see what happens. You usually know something is on the way as she quite often releases "trailers" and snippets of songs and then suddenly out of nowhere her next epic release is here.
I wouldn't get too hung up on the date the press are quoting as her label don't always stick to dates she quotes. Lets just call it around about early May and see. She's due to tour America from April onwards so I would say those shows would be be the best bet for when we'll get to hear the new songs.