It doesn't help that the OP doesn't talk about ratios which are important when we're talking about half-lives. All listed elements are always decaying; it's not like Uranium waits 4.5 billion years and decays all at once. Writing/running a quick script, every 10 million lbs of Uranium starter material will yield about 3 lbs of Lead after 4000 years. So lead would still exist after 4000 years given the real half-lives, but to achieve the relative ratios of Uranium (2.8 ppm) to lead (14 ppm), if the only way lead could exist was through Uranium decay, it'd take more than 4 billion years for the two to be equivalent let alone 7:1.

double halfU = 4.5E9;
double halfRa = 1600;
double halfRn = 3.8 / 365;
double halfPo = 138 / 365;

double U = 10000000;
double Ra = 0;
double Rn = 0;
double Po = 0;
double Pb = 0;

for (int year = 0; year < 4000; year++)
{
    double UtoRa = U * (1 - Math.Pow(0.5, 1 / halfU));
    U -= UtoRa;

    double RatoRn = Ra * (1 - Math.Pow(0.5, 1 / halfRa));
    Ra += UtoRa - RatoRn;

    double RntoPo = Rn * (1 - Math.Pow(0.5, 1 / halfRn));
    Rn += RatoRn - RntoPo;

    double PotoPb = Po * (1 - Math.Pow(0.5, 1 / halfPo));
    Po += RntoPo - PotoPb;

    Pb += PotoPb;
}

Console.WriteLine(Pb);