The error message gives a strong hint as to what the problem is:
One can see that NonlinearModelFit
tries
$\lambda=-1.13888$ but you want to restrict
$\lambda$ to be greater than zero.
modelinvgauss = PDF[InverseGaussianDistribution[\[Mu], \[Lambda]]];
invgauss =
NonlinearModelFit[
datanew, {modelinvgauss[x], \[Lambda] > 0}, {{\[Mu],
10}, {\[Lambda], 10}}, x];
invgauss["BestFitParameters"]
(* {\[Mu] -> 11.098760475474151, \[Lambda] -> 35.72763989840714} *)
Show[ListPlot[datanew, PlotRange -> {{0, 20}, {0, 0.12}}],
Plot[invgauss[x], {x, 0, 20}]]
The fit isn't so great. I have to wonder why you want to fit a probability density function using a regression. Usually a probability density function is fit with a random sample from that distribution. If what you have is really a regression and you're just interested in the form of the density function being an inverse Gaussian, then usually translation and/or scaling parameters are usually added.