This needs some clarification. The next day's growth is not another generation; it is the same plant coming up again after some chastening. It is in fact perfectly possible for plants to adapt to frequent mowing, typically from habitual grazing, by growing shorter, or by growing short-stemmed flowers. The thing is that tall flowers are more successful at pollination, but they also are more vulnerable to grazing. (Ask the Australians about what they call the "tall poppy syndrime"!)
Such plants commonly are found on islands where giant tortoises graze. Plants like dwarf sedges bear their flowers and seeds practically at ground level, whereas related plants on neighbouring islands or the mainland, where there is less concentrated obsessive grazing, bear their seed heads high, where the wind can catch them.
But what happens on your lawn is different, in the short term anyway. Your dandelion grows high when undisturbed, but as soon as it is severely cut back, its damaged tissues pass down a growth control hormone that tells the tissues to buckle down and produce more reproductive organs, fast, but make them short. This reaction is an adaptation suited to an environment where the plants are grazed frequently, but not consistently. Fast reproduction is more likely to escape grazing, and low-growing flowers are less likely to be grazed. If you were to collect the seeds of a low flower and plant them in a place where they were not disturbed, they would at first produce tall flowers. If you then got busy, with scissors or mowers, they would regenerate short flowers again, just as happened under your mower on the lawn. It was exhibiting an already existing adaptation, not a new one.
Presumably if you then carried on with consistent, obsessive mowing for perhaps hundreds or thousands of generations, you would very likely produce plants that grew low unconditionally. They would do well, and outcompete tall growers in grazing, but would be overgrown where grazing was unusual and lush growth could smother competion and attract pollinators more readily.
Simple?
Not really when you get into it!
Jon
