Main.elm

type FrontendMsg
    = FNoop
    | Increment
    | Decrement
    | OnBackendMsg ToFrontend

update : FrontendMsg -> Model -> ( Model, Cmd FrontendMsg )
update msg model =
    case msg of
        FNoop ->
            ( model, Cmd.none )

        Increment ->
            ( { model | counter = model.counter + 1 }
            , sendToBackend CounterIncremented
            )

        Decrement ->
            ( { model | counter = model.counter - 1 }
            , sendToBackend CounterDecremented
            )

        OnBackendMsg (CounterNewValue newValue) ->
            ( { model | counter = newValue }
            , Cmd.none
            )

updateFromBackend : ToFrontend -> Model -> ( Model, Cmd FrontendMsg )
updateFromBackend toFrontend model =
    update (OnBackendMsg toFrontend) model

app =
    Lamdera.Frontend.application
        { init = \_ _ -> init
        , update = update
        , onBackendMsg = updateFromBackend
        , view =
            \model ->
                { title = "Lamdera board app"
                , body = [ view model ]
                }
        , subscriptions = \_ -> Sub.none
        , onUrlChange = \_ -> FNoop
        , onUrlRequest = \_ -> FNoop
        }

This shows how to reroute msgs from the updateFromBackend function into the normal update function, in case someone wants to do that.