You can try to flush out the freehub body with WD40 or a solvent, after your remove the body from the hub. Then lube with a heavy oil or light grease through the annular space. A grease injector is probably required. But this may just be a temporary fix. I've used Phil Wood Tenacious Oil (relatively heavy and sticky) to lube a freehub body, but it was only temporary.

It'll probably be worth buying a new freehub. Depending on the freehub brand, I'm guessing they're about $30 (at least my Bontrager costs that at the LBS). You need to match the freehub body to the hub. And match the casette to the freehub body (most likely Shimano compatible based on the 1070 cassette. If you can remove it (fairly easy) you can probably take it to an LBS for a match,

BTW - 1070 is a great cassette.