No. Like I have never heard anyone in real life compare these 2, it's mostly on ATRL. Lana is still relevant and her next album will have amazing openning numbers, while Lorde is doing her thing and will probably score another hit with Team. Their success is really not related.
I feel like "Summertime Sadness (Cedric Gervais Remix)" mildly smashing would've been more respected if "Royals" hadn't come along and overshadowed it, so possibly.
There's no reason they can't co-exist though. They're popular in different regions and make a different type of music.
No. People on here need to understand that you are not being overshadowed or replaced by somebody else as long as you make music that people are willing to pay for. The casual music buyer doesn't give a **** as long as he likes what he hears.