data = {{0.3, 3}, {0.4, 2.25}, {0.5, 1.8}, {0.6, 1.5}, {0.7, 1.3}, {0.8, 1.2}, {0.9, 1.15},
{1, 1.13}, {1.1, 1.12}, {1.2, 1.11}, {1.4, 1.09}, {1.6, 1.07}, {1.8, 1.05}, {2, 1.03}};
L0 = ListPlot[data, Frame -> True, Axes -> False, Joined -> True,
     Mesh -> All, PlotRange -> {{0.28, 2.02}, {0.98, 3.04}},
     ImageSize -> 550]

nlm = Normal[NonlinearModelFit[data, a + b/(c*x^2), {a, b, c}, x]];
P0 = Plot[nlm, {x, 0.3, 2}, PlotStyle -> Red];
Show[{L0, P0}]