lattice with predicted values

Dear lattice wizards,

I am trying to figure out how to plot predicted values in xyplot,
where the intercept, but not the slope, varies among conditioning
factor levels. I am sure it involves the groups, but I have been
unsuccessful in my search in Pinhiero and Bate, in the help files, or
in the archive, or in my attempts on my own.

My example follows:

FACT is a factor with levels a,b,c
COV is the covariate

mod ~ lm(Y ~ COV + FACT)


#The following draws the right predictions if the relation is the
same for all factor levels, but I can't figure out how to have the
same slopes but different intercepts.

# Function to draw predictions in xyplot

panel.predfinal <- function(mod, x, y) {
     xfit <- seq(min(x), max(x), length=21)
     yfit <- predict(mod, newdata=data.frame(COV=xfit))
     llines(xfit,yfit,lty=1) }

xyplot(Y ~ COV | FACT,
             panel=function(x,y,groups,subscripts){
             panel.xyplot(x,y)
             panel.predfinal(mod,x,y) }