My itinerary was vce-fra-arn on Lufthansa and arn-lax on SAS. I booked this as a star alliance award ticket with SQ miles.

After multiple calls back and forth with Lufthansa and SQ where they told me to call the other, SQ said they would sell me the infant lap ticket for the Lufthansa segments and I was now to call SAS. Their call center was closed, so the next day I called them and then did the same routine calling back and forth. Eventually SQ said they had contacted SAS on my behalf and now SAS would know what to do as their would be noted added. Of course they didn’t. SQ then told me to call the Venice SAS office and gave me a phone number that put me into the SAS phone system... no luck.

Then SQ gave me a new number and it turned out to be the SQ office in Rome. She said she would call me back within a few hours, which she did and sold me the infant lap seat for 291 euros.

now I’m on the SAS flight somewhere over Norway and it’s all good.