It might be easier if you post your itinerary, at any rate I had to do something similar with a TP award booked with TK (I know, SQ and LH/SK have nothing to do with it).

I booked the adults on points, then I called TP and I asked to purchase an infant ticket on the same flights. It is important you don't say you want to add the infant to an existing ticket, because only SQ can touch it. You want to purchase a new infant ticket.

Ideally the LH and SK agents will ask you whether you already have a ticket for an adult on those flights, to which point they should be able to link the two. It might take a fair amount of HUACA and/or requesting supervisor help.

Depending where you are located going directly to an LH office or to a good TA might work.

Good luck!