no difference in predict between lm and lmer I have read several posts here on CV, in which mixed model data were plotted this way (using cake dataset):
library(lme4)
library(ggplot2)
mod <- lmer(angle ~ recipe + temp + (1|replicate), data=cake)
newdat <- expand.grid(recipe=unique(cake$recipe),
              temp=c(min(cake$temp),
                     max(cake$temp)))
lmer.pred <- predict(mod, re.form=~0, newdata=newdat)

lmer.plot <- ggplot(cake, aes(x=temp, y=angle, color=recipe)) + geom_line(data=newdat, aes(y=lmer.pred))

However, recently I realized that we could get the same values with a lm model:
mod2 <- lm(angle ~ recipe + temp, data = cake)
lm.pred <- predict(mod2, newdata = newdat)
lm.plot <- ggplot(cake, aes(temp, angle, color = recipe)) + geom_line(data = newdat, aes(y=lm.pred))

My question is whether lmer.plot is an accurate illustration of the linear mixed model? The cake data contains repeated measures (recipe) so mod2 and lm.plot seems wrong, and, by extension, lmer.plot would also be wrong. However, several posts suggest using plots like lmer.plot to illustrate linear mixed model data, so I'm confused.

For the random-effect model you made the predictions with re.form=~0 so you've set random effects to zero, in such a case the only part that you consider is angle ~ recipe + temp, i.e. the same as in fixed-effects model. If you look at summary(mod) vs summary(mod2) you'll see that the fixed effects parameters are nearly the same, hence nearly the same predictions. Your random effects model assumes random intercepts for replicate's so the difference between the models would be just that the regression lines for each replicate would be "shifted" by the intercept. To see the difference between models, show the regression lines for different recipe's.
