Note: I don't use Lit/LitElement, I just use lit-html with vanilla web components.
I don't find a lot of value in the more complex "component" model/wrapper around native web components, though YMMV.
My components are very simple native light-dom web components that have a render() method that calls lit-html render. For reactivity, I just use class properties. On a setter that needs to mutate the dom, I just call render manually.
It's not really any extra lines of code at the end of the day, and it gives me full control over the lifecycle and render cycle of my components. It's also super easy to debug.
I've used different routers over the years, currently I'm using Vaadin, but I've used Ionic's and others. I may try out the new router that's in Lit/labs.
I'm very satisfied with it. No framework churn, no complex builds, easy debugging, lighting fast performance, minuscule js downloads, easy authoring and vscode has magical tooling support.
lit-html is one of my all time favorite pieces of tech.