Never come across this with any of my four (they all learned in our local indoor snow dome) when booking lessons, and we started three of them at four years old and the oldest at six. Using a chairlift is much easier than using a drag lift anyway! As others have said, they just plonk them on the lift. Often the instructor will accompany children who seem to find the chairlifts a bit tricky; we usually spotted ours next to the instructor on the lift a lot in the first week on the mountains!
The only "complaint" we ever had from ski schools was that our children were - initially - often the slowest in the group to begin with, as they were used to snow dome distances, not big wide blue runs that go on for miles. That would only last a day or so though, and frankly after a week on real snow, the snow dome is ruined for them forever as they get down it in no time now!
Just say she's had a week on snow already, perhaps with a different ski school if you can't change their minds! Often the office staff can't get their heads around the concept of snow dome lessons, as they're set up to measure experience by weeks on snow. We stopped telling them about the snow dome lessons by child 3 as it had got quite awkward trying to explain it with the first two, and just said "a week" for child 3 + 4.
In fact, as another poster said, they tend to sift them in the first hour or so anyway, and I guarantee the instructors doing the sifting won't know (or care) about what the office has said about needing chair lift experience. Honestly with many ski schools there seems to be very little communication between office and instructor at all, children chop and change classes often multiple times in a week with very little fanfare. They'll pluck out the ones who can do controlled turns and stop, and they'll be in the lift queue before you know it!
The lifties are very good at spotting nervous children, especially at the start of ski school for the week, so even if the instructor doesn't notice, I am certain she'll be plonked on a chairlift by a kind liftie, who might well get the attention of the instructor to warn them, and they probably radio ahead to the top to keep an eye out there too. We often look out for our children in ski school and lifts are an easy place to spot them - they definitely look after them until they have it nailed down! They do a far better job with them as beginners than we do with them on the lifts, that's for sure 
I think the only place I have heard of with indoor chair lifts is in Dubai!