Is the lambda term also placed into the new processes’s mailbox, like a startup message?
Let’s find out:
iex(12)> pid = spawn fn -> :timer.sleep(10_000); IO.puts("Messages I've got so far:"); flush(); end
#PID<0.130.0>
iex(13)> send pid, :hello
:hello
Messages I've got so far:
:hello
So the answer is no 
flush is useful to know what’s in the inbox of the current process.
how important is understanding these low-level details for the day-to-day programming of Elixir?
If you’re going to do any concurrent programming with Elixir, it’s very important to go through these details to build a solid mental of how processes work in Elixir. If you just want to build a traditional webapp with Phoenix, you can probably ignore them for now.
