non Lwt version:

let () =
  let parent_pid = Unix.getpid () in
  Printf.sprintf "Parent pid:%d" parent_pid |> print_endline;
  let some_func () =
    Printf.sprintf "Process: %d" (Unix.getpid ())
    |> print_endline
  in
  let marshaled = Marshal.to_bytes some_func [Marshal.Closures] in
  let (read, write) = Unix.pipe () in
  let pid = Unix.fork () in
  (* Child *)
  if pid = 0 then begin
    let in_chan = Unix.in_channel_of_descr read in
    let func : unit -> unit = Marshal.from_channel in_chan in
    func ()
  end
  else begin
    Unix.write write marshaled 0 (Bytes.length marshaled) |> ignore;
    some_func ();
    exit 0
  end

prints:

Parent pid:3760
Process: 3760
Process: 3761


Lwt version:

let program =
  let parent_pid = Unix.getpid () in

  Printf.sprintf "Parent pid:%d" parent_pid
  |> Lwt_io.printl
  |> Lwt.ignore_result;

  let some_func () =
    Printf.sprintf "Process: %d" (Unix.getpid ())
    |> Lwt_io.printl
  in
  let marshaled = Marshal.to_bytes some_func [Marshal.Closures] in
  let (read, write) = Lwt_unix.pipe () in
  let pid = Lwt_unix.fork () in

  (if pid = 0 then begin
    let in_chan = Unix.in_channel_of_descr (Lwt_unix.unix_file_descr read) in
    let func : unit -> unit Lwt.t = Marshal.from_channel in_chan in
    func ()
  end
  else begin
    Lwt_unix.write write marshaled 0 (Bytes.length marshaled)
    |> Lwt.ignore_result
    |> some_func
    |> Lwt.ignore_result;
    exit 0
  end)

let () = Lwt_main.run program

Parent pid:3648
Process: 3648
Parent pid:3648
Process: 3649