Is there a way of doing this within the tidyverse? I do not want to reinvent gunpowder.

data_frame_explosion.R

library(dplyr)

explode <- function(df, f) {
  df_indexed <- df %>% mutate (explosion_index=1:n())
  f_indexed <- function(row_indexed) {
    return(f(row_indexed) %>% mutate(explosion_index=row_indexed['explosion_index']))
  }
  expansion <- df_indexed %>% apply(1, f_indexed) %>% do.call(rbind, .)
  explosion <- df_indexed %>% 
    left_join(expansion, by='explosion_index') %>%
    select(-explosion_index)
  return(explosion)
}

f <- function(row){
  return(data_frame(sample_index=1:row['sample_size'], 
                    sample_value=rpois(row['sample_size'], 
                                       row['lambda'])))
}

df <- data_frame(sample_size=c(2, 3, 5), lambda=c(0.5, 0.1, 0.7))

df %>% explode(f) 

# A tibble: 10 x 4
# sample_size lambda sample_index sample_value
# <dbl>  <dbl>        <int>        <int>
# 1           2    0.5            1            1
# 2           2    0.5            2            1
# 3           3    0.1            1            0
# 4           3    0.1            2            0
# 5           3    0.1            3            0
# 6           5    0.7            1            1
# 7           5    0.7            2            3
# 8           5    0.7            3            0
# 9           5    0.7            4            1
# 10          5    0.7            5            1

Not tidyverse, but expand.grid() ?