If anything, I would rather suggest getting the HE-500 over the LCD-2 for you. Especially used, they go for around $500-$600, half the price of Audeze with taxes, shipping and customs (depending on where you live) - Hifiman's are more lenient.
HE-500 work well with everything. If you have the money for them, I would highly suggest getting these. Seriously, why start at the bottom when you could be over here?
HE-500 are the one headphone that most people, including me, will like and get used to at the first instant. LCD-2 were a learning process for me. HE-500 out of the box (with some burn-in) will blow your mind away if you haven't heard a high end or even a mid entry level phone before.
Save money and time and get these. I understand trying bit by bit and figuring out your preference along the way and would recommend it as well, given that the HE-500 didn't exist. Regardless of the genre you listen to, these will suffice. You'll thank me later and so will your wallet in the long term.