Context: Gym crush I see all the time when I go to the gym. Have had a crush for a while but never had the balls to approach

Last night, I was walking in and saw her at the lockers and decided to say f it. I introduced myself, got her name, we both admitted to seeing each other around and I asked her if she’d like to get coffee sometime. She responded with “I would but I have a boyfriend” ( i could sense she was probably lying) and I said “no worries, sorry to interrupt “ but as I was walking aways she started asking me questions as I was putting my airpods back in. She said “so do you live around here” and I was like “yeah I do, I hope you have a good new year”. I couldn’t tell if she was still trying to keep convo going, and I didn’t feel comfortable asking her personal questions like “do you live around here too” after knowing she has a man. Thoughts?