I can't think of an example where a lawn wouldn't consist of grass, but you can definitely have grass growing (sometimes unwanted!) without it being a lawn. The difference is that a lawn consists of grass that is intended to be groomed (maintained at the same height, perhaps watered, etc.).
A meadow is a natural open area, devoid of trees that may have naturally occurring grasses and/or flowers. A field is typically bigger than a meadow, and may (or may not) have crops cultivated on it. One example of an exception would be a soccer or football field (pitch), but that is maintained for a particular purpose, unlike a meadow that isn't maintained by people. (The only example I can think of where a meadow is "maintained" is in a pseudo-natural environment, perhaps a zoo, where the area is intended to mimic a wild setting.)
I think you can have a lawn that is not grass but it would be qualified in some way. For instance, there is a book called The Camomile Lawn and various ecological bodies encourage wildflower lawns for biodiversity. But I agree that a lawn (unqualified) = mainly grass. Lots of moss in mine!