Thou shalt not kill is not really the same as "thou shalt not murder". "Murder" is completely dependent on the law and actually varies from any place. So what might be justified in one place when it comes to killing may not be in another, and vice versa. So saying "thou shalt not murder" would be very bad as a commandment since it would all depend on what place you were in at the time and the laws of that place. But then that would mean that going to "thou shalt not kill" would not be completely covered in our laws, since we (the US) allow for certain justified killings, such as in defense of self or someone else or even property, during war, even as punishment. So it would need a qualifier to even fit as being the basis of our laws "thou shalt not kill unjustifiably", and even then there is some sort of law preventing some sort of killings in pretty much every culture, even those who have never heard of the Bible or 10 Commandments.
I covered adultery. Due to the Lawrence decision, it is not likely that adultery laws (outside of the military at least) would stand up to a constitutional challenge if they were ever enforced criminally (a person hasn't been charged with adultery outside of the military in the US since 1983). The fact that they haven't been enforced in 30 years pretty much tells us that out justice system doesn't even truly believe that criminal adultery laws are likely to stand up to a challenge.
Stealing is sort of like the killing/murder thing. While stealing is illegal in most cases, it can be argued that we don't consider everything when it comes to stealing as actually stealing. For instance, there are some that claim taxes are stealing. There are others that believe that all land belongs to everyone or no one, and so either a) owning land in itself is stealing or b) things like taking food off of either public land or even private land wouldn't be stealing since everyone should be able to take such things. But it also goes back to pretty much every culture also having some laws against stealing, without inspiration from the Commandments.
The lying thing you nailed. It is not covered in the vast majority of our laws and the only time it is is when it can cause measurable harm to someone, like getting them punished for a crime or avoid justice, or when used in combination of stealing something from someone else.
Thou shalt not covet to most is referring to wanting what your neighbor has. This is in no way illegal. It would be thought policing to make it illegal. In fact, it is almost a tenet of capitalism to want something your neighbor has or even something better than your neighbor has.