Maybe this will work?

.github/workflows/test.yml

@@ -18,6 +18,26 @@ jobs:
       - run: DJANGO_PATH=${GITHUB_WORKSPACE}/django docker-compose build --pull ${{ matrix.compose_app }}
       - run: DJANGO_PATH=${GITHUB_WORKSPACE}/django docker-compose run ${{ matrix.compose_app }}
 
+  sqlite-windows:
+    name: sqlite-windows
+    strategy:
+      fail-fast: false
+      matrix:
+        python_version:
+          - 3.6-windowsservercore-ltsc2016
+          - 3.7-windowsservercore-ltsc2016
+    runs-on: windows-latest
+    steps:
+      - uses: actions/checkout@master
+      - run: git clone https://github.com/django/django.git --depth=1 ${GITHUB_WORKSPACE}/django
+      - run: docker-compose pull --include-deps sqlite || true
+      - run: DJANGO_PATH=${GITHUB_WORKSPACE}/django docker-compose build --pull sqlite
+        env:
+          PYTHON_VERSION: ${{ matrix.python_version }}
+      - run: DJANGO_PATH=${GITHUB_WORKSPACE}/django docker-compose run sqlite
+        env:
+          PYTHON_VERSION: ${{ matrix.python_version }}
+
   sqlite:
     name: sqlite
     strategy:

Dockerfile.windows

@@ -0,0 +1,7 @@
+ARG PYTHON_VERSION
+FROM python:${PYTHON_VERSION}
+
+COPY --chown=test:test tests/requirements/ c:/requirements/
+RUN $files = @(Get-ChildItem c:\requirements\*.txt); \
+    foreach ($file in $files) { pip install -r $file }; \
+    pip install flake8 flake8-isort sphinx pyenchant sphinxcontrib-spelling selenium unittest-xml-reporting

docker-compose.yml

@@ -30,13 +30,28 @@ x-postgres-base: &postgres-base
 services:
   sqlite:
     <<: *base
-    environment:
-    - DJANGO_SETTINGS_MODULE=settings.test_sqlite
+    build:
+      context: ${DJANGO_PATH}
+      dockerfile: ${PWD}/Dockerfile
     entrypoint: python tests/runtests.py
     depends_on:
     - memcached
     - memcached2
 
+  sqlite-windows:
+    <<: *base
+    build:
+      context: ${DJANGO_PATH}
+      dockerfile: ${PWD}/Dockerfile.windows
+      args:
+        - PYTHON_VERSION=${PYTHON_VERSION}
+    environment:
+      - DJANGO_SETTINGS_MODULE=settings.test_sqlite
+    entrypoint: python tests/runtests.py
+    depends_on:
+      - memcached
+      - memcached2
+
   sqlite-gis:
     <<: *base
     entrypoint: python tests/runtests.py