Barry, is it possible you accidentally used the beta 4?  I ran the test suite with a freshly built 3.10, but by mistake was still using the beta, and was surprised.  Once I really got the latest build in place (Python 3.10.0b4+ (heads/3.10:47695e3c88, Jul 15 2021, 11:55:52)), I got these results:

platform darwin -- Python 3.10.0b4+, pytest-6.2.4, py-1.10.0, pluggy-0.13.1
cachedir: .tox/py310/.pytest_cache
rootdir: /System/Volumes/Data/root/src/foo/bug1187/flufl.lock, configfile: setup.cfg, testpaths: test, docs
plugins: cov-2.12.1
collected 108 items

test/test_api.py .                                                                                                                                          [  0%]
test/test_lock.py ...........................                                                                                                               [ 25%]
docs/using.rst ................................................................................                                                             [100%]

======================================================================== warnings summary =========================================================================
.tox/py310/lib/python3.10/site-packages/sybil/integration/pytest.py:58: 80 warnings
  /System/Volumes/Data/root/src/foo/bug1187/flufl.lock/.tox/py310/lib/python3.10/site-packages/sybil/integration/pytest.py:58: PytestDeprecationWarning: A private pytest class or function was used.
    self._request = fixtures.FixtureRequest(self)

-- Docs: https://docs.pytest.org/en/stable/warnings.html

---------- coverage: platform darwin, python 3.10.0-beta-4 -----------
Name                      Stmts   Miss Branch BrPart  Cover   Missing
---------------------------------------------------------------------
flufl/lock/__init__.py        5      0      0      0   100%
flufl/lock/_lockfile.py     253      0     80      0   100%
---------------------------------------------------------------------
TOTAL                       258      0     80      0   100%
Coverage XML written to file coverage.xml

Required test coverage of 100.0% reached. Total coverage: 100.00%