There are lots of different philosophies for how you should distribute that money. Some people here believe that the bulk should be spent on the source. Others believe you should buy the best headphone possible, and spend the rest on source/amp. I fall in the latter camp. If this is a purely home-listening audio system, and you're ok with an open headphone, I would build my system around the HD800 (which I think is a better headphone than the LCD-2).
If you need new, I would spend around $700 on a DAC and around $700 on an amp (I don't have any recommendations in that range as I haven't heard most of those products). If I were you, I would think about three more things:
First, consider buying used. If you go that route, you can have something like Benchmark DAC1 USB --> Luxman P1 --> HD800 for close to $3K. That would be a very nice system. I think the Benchmark is great, but underrated here (and most hi-fi audiophile websites). I've had a great experience with some of that pro gear, and would buy a Benchmark, Lavry, Mytek, Zodiac, etc. before any audiophile fluff. Pair it with a nice warm amp like the P1, and you're in good shape.
Second, if you're sure you want to go the speaker route in the near future and will be listening primarily on speakers (and I went from headphones to speakers and enjoy speakers infinitely more than headphones), I would seriously consider a headphone amp that will double as a good preamp down the line. If you are willing to give tubes a shot, I would say the Eddie Current Zana Deux is your best choice. It sounds great with the HD800, and is a wonderful preamp. A cheap DAC (e.g. Schiit Bifrost) + Zana + HD800 would be a terrific combination.
Third, think about Stax. When I do pull out headphones these days, it's almost always electrostats. You can buy something like the Woo GES for $1500, a Stax 507 for $1000, and pair them with a $500 DAC (I don't know, DACMagic, or DACit, or whatever is hot these days in the $500 range) and have an amazing sounding system.
Lots to think about, but if you're spending that much money, it's worth doing the research and maybe even hearing some of that gear first. Good luck!