Lacto-fermentation which  uses no vinegar, just a salt and spice brine,   is
the oldest method of pickling cucumbers.     During this process,
lactic-acid bacteria preserve the food by converting carbohydrates present
to acetic acid which preserves the food and accounts for the sour taste.
These bacteria are  health-producing, somewhat akin to the live cultures in
yogurts and things like that.  They aren't toxic like I saw someone mention

If you are looking for a pickle juice comparable to modern pickle juice you
don't want to use lacto-fermentation even though that might be more period.
The liquid leftover from the lacto-fermentation process is not the same as
the pickle-juice from modern pickles which is full of vinegar.  It is more
similar to the whey solution leftover when making cheese and it has a lot of
lactic acid in it.  I don't think that it would have  the same health
benefits to the fighters and it certainly doesn’t taste the same.  

If you are looking for a source for documentation:  In 1577, Thomas Hyll
detailed a method of vinegar pickling  purslane using verjuice and salt in
The Gardeners Labyrinth.  I should note though that when  it came to
cucumbers and turnips, he still  recommended the salt and water
lacto-fermentation method.     In 1699, you see John Evelyn detailing a
vinegar process for pickling cucumbers  in Acetaria, that starts with Beer
Vinegar which is an interesting thing to make, also. 

Just as a note, the vinegar you buy in the store now is pretty routinely
distilled.  The raw vinegars like Braggs are the equivalent of what would
have been being used in the Middle Ages.  So you would want to use something
like this  or homemade verjuice or wine vinegar to achieve  period results.
I tried Evelyn's method using the modern vinegar once and it was not as