adding device size-independent y=0 line to a lattice plot

Using the following lattice plot as an example, I would like to add
horizontal lines where y=0:

library(lattice)
library(grid)
fac <- gl(4,12)
x <- letters[rep(1:3,16)]
y <- runif(48,min=0.0)
dotplot(y~x|fac)

I've tried it with grid.lines using npc and native units, which works
fine unless I change the size of the output device - then the lines
are in the wrong place.  Is there a way to do this that is independent
of the output device size?