at the lake simply roll the carpet out into the water and forget it, over time the carpet will trap the finer "sands or silts", it will assist with aquatic vegetation growth whilst it makes the sharpness of the volcanic stone much more tolerable to sit a boat on and walk on too, the best bit is it will slowly breakdown over time and wont be an issue to the environment as it does so....
that may be one solution but unless you own the lake, that's called criminal dumping and in Maricopa County AZ. is a crime with up to 6 months imprisonment & $2,500 fine or to one year if charged as a Class 6 Felony –
Also carpet is typically made of plastics and nylons... not exactly free of "issue to the environment" - i would be pissed if someone threw that in my local waterways
