I just checked
www.swiss.com and found this.
Passengers eligible to access the Arrival Lounge appear to be:
First Class SWISS & Lufthansa
Business Class SWISS & Lufthansa
HON Circle
Senator : only SWISS Senators
Frequent Traveller : only SWISS Frequent Travellers
So it looks like SEN and FTL without the SWISS logo on their card cannot access the Arrival Lounge if travelling in Y.