I think we're talking about two different things here.

There is a paid membership to United airport lounges or "United Clubs." Sometimes you will get a couple of day passes to these clubs as a benefit for having one of the Chase credit cards.

Then there is the Star Alliance lounge access you get for holding the United Mileage Plus "Club" card. You get a separate Star Alliance lounge club card that you show to gain access.

The first scenario gives you access to United Clubs only. The second scenario gives you access to United lounges and other Star Alliance lounges. If you hold the Star Alliance lounge access card they should let you into the Turkish lounge.

The United Club card (second scenario) does come with a hefty yearly fee. I think its $400-$450 now. But there are targeted offers that waive the first year fee. The way I got targeted was to google the card a couple of times, then log into my Mileage Plus account. The offer appeared after I logged in.

This card also gives 1.5 mi/ $1 spend which is nice.