How can I make a collapsible chair float on a lake?

One way I can think of is to use a mirror or something reflective that is placed in front of a platform that have the collapsible chair fixed on to as you need. The mirror needs to be placed at a certain angle so that the viewer see whats reflected by the mirror, and, see what actual is "in front of the mirror". This would cover what's behind.

Or you try to reproduce this kind of principle https://i.ytimg.com/vi/YCHvpf2gDIk/maxresdefault.jpg or the "levitating man" that can often be seen on the streets.

The helping structure can be aligned along the chair's backside-face and just needs a fixing beneath the water

Stable floating sounds challenging.

A few magicians have done "walking on water" stunts over the years, and the general consensus is that they're doing it by having a sheet of plexiglass suspended just below the surface, somehow. Having it below the surface means the water surface ripples etc. are mostly unaffected.

I'd find a relatively shallow lake, and hammer 4 wooden stakes into the lake bed (power tools for post-hammering exist), until the tops are just below the surface. You could start with longer-than-needed wooden stakes, hammer them in a bit, cut off the extra and then hammer the final distance. I suppose you could skip the plexiglass and put the chair legs directly onto the stakes, if they were positioned well enough.