Summarizing the fitted model takes more RAM than

Note that the fitted method in lme had a level= argument that is no
longer available in lmer presumably because lmer does not assume
a hierarchy -- but do we have or will we have an easy way to get the
same effect as fitted(..., level=) in lmer?

library(nlme)
# example from plot.lme
fm1 <- lme(distance ~ age, Orthodont, random = ~ age | Subject)

fit0 <- fitted(fm1, level = 0)
fit1 <- fitted(fm1, level = 1)

(Maybe this is a bad example since its actually not so hard:
   fitted(lmer(distance ~ age + (age|Subject), Orthodont))
gives level 1 and
  fitted(lm(distance ~ age, Orthodont))
gives level 0 but even here it involved the complexity of using different
approaches to get them whereas with lme one could do it in a
unified manner.)

I believe you are using the terminology of multilevel modeling where
one characterizes factors as being at the first level, the second
level, etc.  One can fit multilevel models using lmer but one can also