Mine sometimes does in a lift -I remember very clearly going in the Twin Towers lift many years ago and the lift operator said jokingly (chillingly now) that "if one Tower falls the other will too" -said with a broad grin.
That lift and another in New York were very high and fast and left my heart down somewhere way below.
Escalators are not a problem except that sometimes I get scared as I near the top, for what reason I do not know.
Occasionally....I'm a very clumsy girl so my heart lurches on escalators frequently as I regularly nearly fall over. In lifts, I'm fine but in my work lift I go up 39 floors and occasionally when it zips up super fast I get a bit woozy!
They don't usually bother me. However, I remember one time years ago my husband and I were in a lift in a Singapore Hotel which freaked me out. It was a glass lift on the outside of a high-rise hotel and we travelled down to the ground in it. Really scary as I don't have a head for heights. I ended up facing the back wall of the lift for the entire journey as I just couldn't look out the front of the lift, which my husband said had a spectacular view - I took his word for it!
Yes, I was terrified of the escalators, before I started work at DJ's, in Sydney, as a teen. Even now, at some railway stations, my heart misses a beat, when I look down to the bottom of the top! As far as lifts go, it's only the glass lifts that scare me, even on cruise ships! Not the 1 in the Apple shop on 5th Ave though, as that only goes down 1 floor, from the road. The whole shop is made from glass. Wonderful!