with gganimate and tweenr

using \(\lambda\) from 5 to 55 with a step of 5.
library(tidyverse)
library(gganimate)
library(tweenr) # devtools::install_github("thomasp85/tweenr")

crossing(tibble(x = 1:50),
         tibble(lambda = c(2, seq(5, 55, 5)))) %>%
  mutate(dpoi = dpois(x, lambda = lambda)) -> poi_df

my_list <- map(unique(poi_df$lambda), ~ filter(poi_df, lambda == .x) %>% as.data.frame())

tween_states(my_list, tweenlength = 7, statelength = 1, ease = "cubic-in-out", nframes = 50) %>%
  
  ggplot(aes(x, dpoi, frame = .frame)) + 
  geom_col(position = "dodge", width = 2.0) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(x = NULL) +
  theme_classic(16) -> p

gganimate(p, title_frame = FALSE, ani.width = 600, ani.height = 450, interval = 0.1, filename = "poisson.gif")