Extrapolating from a LOWESS or LOESS fit is a very bad idea.
LOWESS works by fitting a weighted linear model to a local subset of the data.
You find the "N" nearest neighbors to your data point. You then fit either a first order or second order polynomial to the data, weighting the regression based on the distance from the data point.
This local regression model is used to estimate a value for your original data point.
You repeat this same process for all of the data points in your sample.
Interpolation is pretty safe (and easy). Connect all your data points with a PCHIP and you're off to the races.
On the other hand, extrapolation is a VERY bad idea. Your local model is based on a very small subset of the data. Your projection is going to be incredibly sensitive to whatever type of assumption you make about your data.
Ultimately, you need to make some kind of assumption how to extrapolate from those last few end points. Consider how radically your estimation might change depending on whether you used linear interpolation as opposed to PCHIP as opposed to a cubic spline.