Now, suppose the transformation(in 2d) I am working with has two
separate functions for $x$ and $y$.
That is, the transformation for $x$ is of the form $$ x'=\frac{x}{x+y} $$ and the transformation of $y$ is $$ y'=\frac{y}{x+y} $$ Each is an LFT (The schwarzian derivatives are $0$) but is
the transform as a whole still considered an LFT?