The solution is to go to 'Text styple' after right click on 'selected' text. Then go to 'customize'.
This is pretty obscure. To me style and size are not the same thing. At least size control is there. Choice of 'sizes' is relatively crude, but good enough ...
This would work for footnotes too though it might get tedious if you've got a lot of 'em.
-Traruh
LyX ⇒ Footnote font size in lyx
