The most economical way is not to mix and match airlines. To Tokyo, just book ANA both ways and use Virgin Atlantic miles.
Roundtrip ANA First Class between IAD-TYO is just 120,000 Virgin miles (transfer from Amex, Chase, etc...). Must be purchased as a round-trip. No one way awards.

Forget LH for now. You can't use miles until inside 2 weeks and LH has just cut all First Class to the US with no indications when it might return.
And even if you could magically find award seats, they would be priced more than double the Virgin price.