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I don't think they do, at least not in a sustained way. Dalton has some pictures in his book that do show both lacewings and flies flying upside-down, but only as part of a take-off manouvre. I'm sure it is only for a brief time until they right themselves.
I tried to make it clear in my description of the house-fly ceiling manouvre, that it flies right-way-up, and only turns upside-down when landing.
[Actually insects flying upside-down I can cope with - it's watching helicopters flying upside down that really spooks me! :D ]