American Idol is the best possible option for promo.
1. You can pre-record your performance.
2. You can record it more than 2 times,when Katy was pre-recording her E.T. performance she was recording it 2 times,she wasn't happy with 1st one.
3. That gives Lana opportunity to be more relaxed and if something goes wrong she can always repeat it.
4. Over 20 million people will watch it so if she performs like she knows, people will get chance to see real her(SNL who).