You can use miles. LH miles easily, and I think for United miles you'll need to the paper voucher United can send you.
To the best of my knowledge does the special LH/UA upgrade agreement covers upgrades from H,M,B,Y class to Biz and from C to First.
The *A Upgrade scheme allows upgrades B,Y to Biz and D,C to First but that one is in limbo for us MP members for the time being.