This is extremely simple, there's no reason to call SAS and check. The membership is personal. Unless there's a credit card involved you can not put your travel on your dads EBG card. The travel will be registered on the credit card you are paying with if you don't have an EB account.

If your dad gives you his DC/MC credit card with EBG, I think he should worry about other things when you are going to the US...

But still, when you are checking in, it will say your name without EBG under the name, so the BP will not be EBG and not give you lounge access. It’s also illegal for you to use a credit card with another persons name since it is a clear violation with the contract between the bank and the owner of the card.

At lounges in Scandinavia, they slide your BP most times in addition to your EBG card and you will be caught right there. At RCCs they are pretty thorough on checking both card and BP

So, there his a huge chance if you get caught, not worth it.

And at the end, you have no business being in the lounge anyways since you are not EBG.