This doesn't work because js imports must reference a specific file with either a relative path or an absolute path, assuming your project structure is something like the following:
/node_modules
/lit-element
/other-library
/src
/components
my-element.js
index.html
From my-element.js
, your import would be
import {LitElement, html} from '../../node_modules/lit-element/lit-element.js'
However, since this kind of configuration is confusing and you'll probably end up setting a build script sometime too, the recommendation would be to keep your imports as they are right now and use a dev server that remaps your imports to node_modules
like open-wc's web server
Update (Feb. 2021): The web server mentioned on this question has gone through a few iterations and improvements. The current package is @web/dev-server
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