what different is between "a lot smaller" "much smaller" "far smaller"?

Question

Answer

a lot-much-far are all used to ''intensify'' the comparison. So they are all the same things in this context.
She is taller than me.(comparison)
She is much /far/ a lot taller than me.( an intensifier is used to make the comparison strong)

Answer

They all mean pretty much the same thing.  The difference is in the formality.
From most to least formal:
far (mostly written)
much (spoken and written)
a lot (mostly spoken)

I myself use these words only if the object or person I'm talking about is 23.7% smaller than the object or person I am comparing to. ;-)