Given that a meadow is a grassland managed by mowing, you could argue that a lawn is a special form of meadow. But a typical meadow is allowed to grow for a few months and then cut for hay when the grass is flowering. Ecologically I’d say a lawn is closer to a pasture, since the grass is kept at the kind of height you would expect under permanent grazing. The suite of flowers is different from a meadow. The lawn flowers are mainly low-growing repeat flowerers such as daisies, self-heal and trefoils. The orchid gets special treatment to let it flower. You don’t generally get waxcaps in meadows.
As for how much of it is monoculture grass, that depends on how you sample it. A 10 cm quadrat would be unlikely to find any monoculture grass but at the 1 square centimetre scale you would be quite likely to find only grass (and moss).
