read_html docs inconsistent with behaviour if lxml not installed

[attack68]

Code Sample, a copy-pastable example if possible

>>> dfs = pd.read_html('<table><tr><td>1</td></tr></table>')
ImportError: lxml not found, please install it
>>> dfs = pd.read_html('<table><tr><td>1</td></tr></table>', flavor='bs4')
[ 0
0 1]

Problem description

The documentation explictly states, in the HTML-parsing-gotchas page and the argument docstring that the fall back is to 'bs4+html5lib' if 'lxml' fails.
For me there is no fallback, just an ImportError since I do not have lxml installed.

Expected Output

Docs should be changed to require explicit flavor input, or the ImportError is caught.

Output of pd.show_versions()

pandas == 0.25.3

[TomAugspurger]

Looks like in

pandas/pandas/io/html.py

Lines 885 to 886 in 37dfcc1

	for flav in flavor:
	parser = _parser_dispatch(flav)

we unconditionally raise an exception, even if the flavor was implicit from None. Will need some logic to handle that case.

[bsipocz]

I've run into this very same problem, where flavor was set to ('lxml', 'bs4') from None, and in the loop it never in fact got to bs4.

Would changing the order of the tuple be controversial, or rewriting the loop? If large/complicated consequences are not foreseen I could open a PR for this.