I know it wouldn't be the most glamorous signing, but personally I would attempt to sign Giroud in the January window. Lampard is unlikely to care about keeping him, he is proven premier league standard, only has 6 months on his contract, has a good relationship with Pogba, wouldn't halt progress for any of our younger players, wouldn't be fazed by the expectation of the club given that he has played for Arsenal, Chelsea and in a WC final for France. I even think he wouldn't demand too stupidly high wages.
He doesn't bang a tonne of goals, but would bring both Rashford and Martial into the game more, and act as the target man that neither of them can really be.