MdlApp.kt

fun mdlApp(init: MdlApp.() -> Unit): MdlApp {
    val app = MdlApp()
    app.init()
    return app
}

class MdlApp() {
    private val app = document.getElementById("MdlApp")

    init {
        requireNotNull(app) { "No MldApp Element found!" }
    }

    fun navigationLayout(content: MdlContent, cssClass: String = "", init: Layout.() -> Unit) {
        val nl = Layout(content, cssClass)
        nl.init()
        nl.mainElement.append(nl.content.content.mainElement)
        app?.append(nl.mainElement)
    }
}

You can get rid of the manual null check in the init block by either specifying the type of app explicitly, without the question mark, or by adding !! after document.getElementById("MdlApp") to assert it's not null. After doing this, you can remove the question mark after app on the last line since it can't be null.