  We prove that in every metric space where no line contains all the points,
there are at least $\Omega(n^{2/3})$ lines. This improves the previous
$\Omega(\sqrt{n})$ lower bound on the number of lines in general metric space,
and also improves the previous $\Omega(n^{4/7})$ lower bound on the number of
lines in metric spaces generated by connected graphs.
