Add styles to override vaadin-date-picker default lumo theme

There are few styles I would like to override in the lumo theme for the vaadin-date-picker, but I don’t see my changes. I can change them directly in the node_modules/vaadin-date-picker/theme/lumo files, and they work, but that’s obviously not going to cut it. Any idea what I’m doing wrong? Here is my code:

import { html, css, LitElement } from 'lit-element'
import '@vaadin/vaadin-date-picker/vaadin-date-picker'
import moment from 'moment';

export class TwaDateSearch extends LitElement {
  static get properties() {
    return {
      date: String,
    }
  }

  constructor() {
    super();
    this.date = ''
  }

  render(){
    return html`
    <dom-module theme-for="vaadin-text-field">
      <template>
        <style>
        [part~="input-field"]
 {
            height: 30px;
            width: 130px;
            font-size: 13px;
            border-radius: 0;
          }
        </style>
      </template>
    </dom-module>

    <dom-module theme-for="vaadin-month-calendar">
      <template>
        <style include="vaadin-month-calendar-default-theme">
        [part="date"]
{
          font-size: 13px;
        }
  
        [part="weekday"]
{
          font-size: 11px;
        }
  
        [part="month-header"]
 {
          font-size: 14px;
        }
        </style>
      </template>
    </dom-module> 

    <dom-module theme-for="vaadin-button">
      <template>
        <style>
        :host {
          color: #2d699e !important;
        }
        </style>
      </template>
    </dom-module> 

    <vaadin-date-picker 
    @change="${this.datePicked}"
    placeholder="ddMMMyy" .value="${this.date}">
    </vaadin-date-picker>
    `;
  }

  datePicked(){
    this.date = moment(this.querySelector('vaadin-date-picker').value)
    this.dispatchEvent(new CustomEvent('datepicked', {}));
  }

  createRenderRoot(){
    return this
  }
}

This whole element is in the shadowRoot of another element, but the styles are contained in this file, so I wouldn’t think that would make a difference.
Any help is very much appreciated! And please let me know if I should provide any additional information.

I figured out my issue. Apparently each dom-module needs an id.