Fawn's secret life

The new neighbour
You meet Fawn for the first time when you pay 2000 to rent condo; she lives the next door from you.

After meeting Fawn, keep talking with her every day, until she leaves you alone in her condo, giving you option to snoop around or leave. From now on, there are several ways to finish up the quest. The way you finish the quest mainly affects Fawn's dialogues, but has no long-terms consequences.

The Torture Rack
There are three ways to learn about Fawn's secret hobbies. Regardless of which method was chosen, in the end she would tell about "The Torture Rack" club, her being a dominatrix here, and offer you to become her sub. While you can refuse, the rest of her route wouldn't become available until you agree.

Stealing the card
Search through her condo until you find "The Torture Rack" club's membership card. Pick up it.

Visit the club and try to ask the receptionist what Fawn is doing here. They wouldn't reveal the private information, but would offer to buy that card back from you. You are free to agree or refuse, that wouldn't have any effect on the rest of the quest, though Fawn would react badly when she finds out. Either way, your only option left is to wait for Fawn until she exits the building, which wouldn't produce any result.

Go home and take some rest, then talk with Fawn again.

Ask Fawn directly
If Lust Doll snooped around, but refused to pick up the card, they may try to ask Fawn about it the next time they talk to her. Choosing to not ask Fawn would just result in the normal talk, allowing you to ask Fawn the next time (the quest wouldn't progress until you do, however), otherwise, Fawn would reveal the truth about the Torture Rack club. Wether she was asked subtly (Speech check) or directly affects only the dialogues.

Spying on Fawn
If the player refuses to snoop around in the Fawn's condo, after being invited to the Roxie's Diner, an event triggers after you walk into a south-western part of the New Ark Slums, causing Lust Doll to spot Fawn going to the back door of the Torture Rack club. You can ask receptionist about Fawn after that.