Two and a half years ago, right after I quit working, I went in to see my family dentist of over 20 years for a regularly scheduled checkup and cleaning. Since I was no longer covered by my former employer's dental plan, my dentist asked if I had changed jobs. Thinking he probably didn't really care too much about my personal situation but was most likely just wanting to make sure he was going to get paid, I told him I was currently between jobs but that I would gladly pay cash for his services, which he seemed fine with.
When I got the bill I was a little surprised that a checkup and cleaning only cost ~$60. I felt a little guilty, afterwards, though, when I thought about it, because it seemed like maybe my dentist had charged me a below market rate because he felt sorry for me because I was "out of work..."
Six months later when I went back in for my next dental appointment, my dentist seemed really surprised that I still hadn't gone back to work yet and therefore still didn't have dental insurance. Since I like my dentist and have known him for a long time, when he asked me during that second visit how my "job search" was going, I told him the truth, that I wasn't planning on having to go back to working at a regular job - ever. After a moment of somewhat awkward silence, my dentist told me he would love to retire but that he didn't think he would be able to for "a long time." We had what seemed to me to be a really good conversation about FIRE and how it works. We talked about index funds, asset allocation, accessing money in tax advantaged retirement accounts before age 59.5, the ACA, etc.
It felt good to tell my dentist the truth, and when I got the bill for his services, that time, it was $120, so double what he had charged me the last time. It seemed, my guess had been right, and my dentist had undercharged me on the previous visit. Of course, I was totally fine and felt much more honest paying the regular going rate for my dentist's services. He works hard and I didn't want him giving me a discount because he felt sorry for me.
Before I actually FIREd, I sometimes pictured future conversations I would have with random people I'd meet in which I would happily tell them that I was retired and explain all about FIRE if they seemed interested. The reality is a little different from my daydreams, though. Like the OP, I don't always divulge everything to everyone all the time. I pick and choose when and to whom I give out information about my work/retirement status. I wouldn't say that I outright lie to people about it. I just, sometimes, don't tell them the entire truth.
Saying to someone I don't know very well and may never meet again, "We're taking some time off and living from savings." isn't a lie. Sometimes, even if I don't know someone very well, if he seems nice and interested, I'll tell more of the truth and explain that at the rate we are spending money from our investments they should continue growing so that we can, hopefully, increase the amount that we spend each year to account for inflation. Sometimes, if people seem to not understand that explanation, I simplify it and tell them that we are, basically, "living off of the interest" from our savings while allowing the principal to continue growing. Although this isn't technically true, it seems to make more sense to some people than trying to explain about capital gains and dividends, which, for some people, apparently sounds like a foreign language...