It isn't actually the voltage which causes ionisation in lifters, it's the high electric field strength.
Ionisation always occurs in pairs, a positive (a cation) and a negative (an anion) regardless of the polarity of the wire. They are always formed in pairs, and always the same number of positive as negative ions.
In the case of a thin wire or sharp pin charged positive, a pair of ions are created close to it (where the field strength is the highest) the negative ion of this pair is attracted to the wire and ceases to exist. The positive ion is repelled from the positive wire and toward anything negative. Which - in the case of a lifter - is the foil 'skirt'.
Regarding powering a lifter with high frequency AC...
The results of my experiments with a 30kHz AC signal (directly from the flyback) resulted in a very small amount of thrust when the lifter which had only one electrode!
It had one corona wire - driven by the flyback transformer - and one collector (skirt) which was made of plastic!
Most of the ions recombined in close proximity to the collector as expected however, some ions (both polarities) headed for the plastic skirt where they recombined. Movement from ions to the plastic skirt resulted in a small amount of thrust.
If testing this configuration, put the plastic skirt extremely close to the corona wire.