In vacuum, the required insulation is cheap and easy: more layers of the famous metallized crinkled plastic foil. The stuff that (with gold-colored metallization) is an iconic part of "the" satellite/space probe design.
The hard part about that insulation is that on earth, you need to sustain a vacuum in the annular space while overall being light due to the LH2 itself being light. Ideas would be to get tension fibers bridging that annular space, the inner tank with the LH2 being slightly pressurized, and thus the outer wall being kept from large-scale buckling (and small-scale buckling is cheap to reinforce for with an isogrid (triangle honeycomb) or other similar reinforcement structure on the outside of it). But in space, the outer wall isn't needed, because space is already a vacuum.
A pure vacuum shuttle should be fine with getting launched and then wrapped with the insulation afterwards.
Launching it empty is likely not really easier than launching it full, due to LH2's low density. But that's not important.
The hard part about that insulation is that on earth, you need to sustain a vacuum in the annular space while overall being light due to the LH2 itself being light. Ideas would be to get tension fibers bridging that annular space, the inner tank with the LH2 being slightly pressurized, and thus the outer wall being kept from large-scale buckling (and small-scale buckling is cheap to reinforce for with an isogrid (triangle honeycomb) or other similar reinforcement structure on the outside of it). But in space, the outer wall isn't needed, because space is already a vacuum.