Schiit Bifrost and Lyr, and a pair of cheap 6BZ7 and be happy with this combo.
I had the LCD2 before and it sounds beautifully with Lyr/Bifrost, if you can invest some rare tubes like Siemens CCa, Telefunken, .... it would take the Lyr to a higher league imho.
Btw, 1100 for a Fostex HPA8C is not a bad deal though, I heard many folks , also Mike - headfonia said the HPA8C has a superb DAC, which I think is justified the $1100 price tag alone. Plus you'll have the headphone amp section, which could not be a top notch, or comparable with some 1k-1.5k headphone amps... But what would you expect more in a 1.1k one-box DAC/amp? It already has a great DAC.
If I have to force to choose the Lyr/Bifrost and HPA8C, I would take the Lyr/Bifrost, and the exceeded money will be spent on tube rolling for funs.