"Clay Targets" ... may well have once been made of clay, but as reported, are now (ands have for my lifetime at least... and that's too many years) consist of pitch & limestone.
In my mispent youth and throughout my middle age ( assuming a lifespan of about 125 years

) ... I've had the occassion to hang around too many gun clubs, including my local one ... and yes they use Lawry Targets alsmost exclusively.
I've been at Clubs, including my own, on and off ( but of course not continuously) on virtually every day of the week, and at every season, sometimes three and four days a week, during all daylight hours, sometimes, dusk to dawn, and often arriving prior to anyone else on site. I have yet to notice... over the past 35 years at least... no profusion of dead and dying wildlife, bird, mammal or amphibian species, or any other critters lying around dead or sick from having ingested pieces of clay targets on the shooting fields.
Where the broken pieces tend to fall, and they do get deposited to a surprising depth over time, particularly at the trap & skeet ranges, grass does not grow well, but neither would it grow well if it were covered up in a blanket of gravel, whether limestone or granite. The black shards are somewhat unsightly, but less so than the bright orange painted parts, which do fade over time and exposure to the elements. More unsightly are the profusion of plastic wads in many shades of colour, which do not seem to degenerate whatsoever.
One acquaintance, a rather wealthy chap at that, has his own Sporting Clay range on
his estate of a couple of hundred acres. He insists on "all black" targets only and on
supplying to his shooting guests, a Kent / Gamebore load with a fibre wad. In having shot there over the past 15 years ... no unsightly build-up of clays, wads lying about and no profusion of dead wildlife either.
Probably far less of a problem than the pesticides and herbacides commonly used for agricultural purposes.