How does Prism create the LOWESS smoothed curves?

Lowess is a method to create a smooth(ish) curve, not a method to analyze data.

Lowess is a family of methods that differ in three ways:

• Q (the proportion of the data being used for smoothing of specific point). This can also be specified as the number of neighboring points to consider when smoothing. This is how Prism works, and it offers three choices. 
• W, the weighting function used for weighted local regression. Prism uses a very standard weighting function: W = 1 / (1 + |DeltaX|^3)^3
• Lambda, the order of the polynomial being used for fitting. Prism fits a straight line. Some methods use polynomials of higher order. 

Prism uses the equations explained in detail in section 4.11 of JC Chambers, et. al, Graphical Methods for Data Analysis, Wadsworth & Brooks, 1983. Scanned copy of those pages.