Why isn't lead-207 radioactive? I've recently learnt from here, in an atom, the stability of an atom is described in two contexts, one according to the ratio of neutron and proton of the atom. The ratio will always be between 1 and 1.5 if proton increases, then the ratio is less than the 1; therefore, the atom becomes unstable. Another context is nucleons in the nucleus.
The nuclei that contain more than 82 protons are extremely unstable. As the number of the proton is very high, so the ratio of neutron and proton becomes less than the one; therefore, the ratio becomes unstable. Every atom in the periodic table moves towards stability. So for attaining stability, the nuclei of 82 protons go for radioactive decay.
Pb-207 has 82 protons and 125 neutrons which indicates that neutron - proton ratio of Pb-207 is greater than 1.5. Then why Pb-207 isn't unstable? (The same question goes for Pb-206 and Pb-208).
 A: A nucleus with $A$ nucleons is most stable with a certain nonlinear relationship between its number of neutrons $N$ and number of protons $Z$, whereby larger nuclei tend to have a larger neutron-to-proton ratio. It's certainly nothing as crude as "maximum 1.5 neutrons per proton", and even what I've linked to is itself only a crude approximation. Nuclear physics is very complicated, because protons and neutrons obey something analogous to electrons' periodic law in chemistry, albeit a version still not fully understood.
The salient detail here is ${}^{207}\mbox{Pb}$ is only one neutron short [sic] of having very good reason to be stable. (Stability isn't a matter of degree, but how energetically disfavoured would be hypothetical decays of a stable nuclide.) You can think of ${}^{208}\mbox{Pb}$ as analogous to being a noble gas twice over, once for protons, once for neutrons. (Before you argue ${}^{207}\mbox{Pb}$ is like a halogen in neutron terms, bear in mind there's no easy source of an extra neutron, so the analogy breaks down there, and doesn't give a reason for the nucleus to be stable.) So it would be downright bizarre for ${}^{207}\mbox{Pb}$ to not manage to be stable.
And while we're at it, lead has two more stable isotopes, ${}^{204}\mbox{Pb}$ and ${}^{206}\mbox{Pb}$. My above link's approximation aside, most proton numbers for a nucleus, especially "magic" ones, allow some leeway in how many neutrons leave it stable. Why ${}^{205}\mbox{Pb}$ is unstable would make an interesting question in its own right; but just to add another wrinkle, that isotope becomes stable if ionized, because its decay is the electron capture $e^-+p^+\to n+\nu_e$, giving ${}^{205}\mbox{Tl}$. Needless to say, if you wonder about the in/stability of a nucleus, you have to ask yourself how you think it would decay.
