Non-grass lawns (e.g. chamomile, thyme and clover) can all be cut with a mower if the area is too large to trim with shears or a nylon-line trimmer. And it's the cutting height range of the mower that is more important than whether it is a rotary or cylinder machine.

Clover will stand close mowing and probably flower between mowing sessions. However, thymes should be left taller and only mown after flowering, otherwise you'll lose the display (the actual cutting height depends on the type of thyme). Chamomile lawns should not be mown closer than 50-75mm (2-3in). So for these lawns, you'll need a mower that can be set with a higher than usual cutting height, so a wheeled rotary mower (not a hover) is your best bet.