I think I now know which model works, so I can answer the question for myself. Both models work, it depends on the subject-variable.

To get a better understanding of which random parts to use, I have computed four models:

    fit <- lme4::lmer(DV ~ group * time + age + education +
                        (1|lfd) + 
                        (1|group:lfd) +
                        (1|time:lfd),
                      data = mydata)
    
    fit2 <- lme4::lmer(DV ~ group * time + age + education +
                        (1+time|lfd), data = mydata)

    fit3 <- lme4::lmer(DV ~ group * time + age + education +
                        (1|subject), data = mydata)

    fit4 <- lme4::lmer(DV ~ group * time + age + education +
                        (1|lfd), data = mydata)


All four models produce the same (fixed-effects) results. `lfd` is a repeating number, which repeats an ID 4 times: once per group and once per time (so 2 groups by 2 time points are 4 groups).

`subject` is a repeated ID for each group in both time points, i.e. I have just 2 groups (group A and B), not further distinguish by `time`.

For me, the quintessence - after trying to better understand 2-way repeated measures with mixed models - is: 
> I think that you don't need to worry about nesting as long as you don't repeat subject ID's within treatment groups.

(as already mentioned [in this answer](http://stats.stackexchange.com/a/59059/54740), but at that time not understood by me. ;-) )