The Oxford English Dictionary (OED, 3^rd edition – 2002) thus defines to wash the milk off one’s liver:

to purge oneself of cowardice. Obsolete.

To illustrate this definition, the OED provides one example only: the proverb “Wash thy milke off thy liuer, (say we)”, from A Dictionarie of the French and English Tongues (1611), by Randle Cotgrave.

But the context of the quotation in this 17^th-century dictionary shows that the definition given by the OED is erroneous. Cotgrave recorded the English proverb as an equivalent of a French one under the headword Laict (“Milke”):

Vin sur laict c’est souhait, laict sur vin c’est venin*:
Prov. Wash thy milke off thy liuer, (say we).

(* The French proverb translates literally as “Wine upon [i.e. after] milk, it is wish, milk upon wine, it is venom.” The choice of the words was determined by rhyme: laict–souhait and vin–venin.)

Under the headword Souhait (“A wish, or desire”), Cotgrave cited the same French proverb, but with a different English equivalent:

Vin sur laict c’est souhait, laict sur vin c’est venin:
Prov. Milke before wine I would twere mine, milke taken after is poisons daughter.

(The meaning of this English proverb is very close to that of the French one. The word mine rhymes with wine and the word daughter with after.)

In the chapter titled Proverbs and Proverbial Observations belonging to Health, Diet and Physick of A Collection of English Proverbs (1670), the English naturalist and theologian John Ray (1627-1705) gave an extended version of the first proverb cited by Cotgrave:

If you would live ever, you must wash milk from your liver.
Butter is gold in the morning, silver at noon, lead at night.
After cheese comes nothing.

Ray added the following remark:

Vin sur laict c’est souhait, Laict sur vin c’est venin. Gall [= Gallic]. This is an idle old saw, for which I can see no reason but rather for the contrary.

But the French saying, as well as the English proverb Milke before wine I would twere mine, milke taken after is poisons daughter, do make sense, as Henry Buttes (died 1632) explained in Dyets dry dinner consisting of eight seuerall courses: 1. Fruites 2. Hearbes. 3. Flesh. 4. Fish. 5. whitmeats. 6. Spice. 7. Sauce. 8. Tabacco. All serued in after the order of time vniuersall (1599):

Eate no more Milke, then you can well digest: though it seemeth to be soft and easie meat [= food], fit for children and milkesops, yet it is not so. Vse no violence after it, nor drinke wine, afore you feele it throughly decocted.

In Les Victimes du lait et du régime lacté (The Victims of Milk and of the Milk Diet –1897), a French physician named Georges-Henri Meunier gave a more scientific explanation of the French proverb; he wrote that ‘vin’ is to be understood as any food, solid or liquid, capable of coagulating the milk arriving in the stomach already in the process of digesting, whereas, when the milk has arrived first, all that comes afterwards will have little effect on it as it is already breaking down.

     original text:
Sous l’expression vin, il faut, à notre avis, comprendre tout aliment, solide ou liquide, d’une composition chimique différente du lait ou du moins capable de coaguler le lait arrivant second dans l’estomac en travail de digestion, alors qu’étant arrivé premier et se trouvant en partie digéré, tout ce qui viendra après, n’aura en général que peu d’influence sur le lait en passe d’être chimifié.

The Dictionnaire universel françois & latin (known as ‘Dictionnaire de Trévoux’ – 1704) misinterpreted the French proverb:

Wine upon milk, it is wish; milk upon wine, it is venom, that is to say, that one wishes to come out of childhood, when one is fed on milk only, in order to get to an age when one drinks wine, & that milk upon wine is venom, because are being fed on milk again those who are seriously ill with consumption and feebleness.
     original text:
Vin sur lait, c’est souhait ; lait sur vin, c’est venin, c’est-à-dire, qu’on désire de sortir de l’enfance où l’on n’est nourri que de lait, pour passer à l’âge où l’on boit du vin, & que lait sur vin est venin, parce que l’on ne remet au lait que ceux qui sont dangereusement malades de Phtysie, & de défaillance.

In Nos vieux Proverbes (Our Old Proverbs – 1886), the French librarian and lexicographer Lorédan Larchey (1831-1902) also misunderstood the French saying:

The true meaning of this last precept has been much disputed. I believe that hygiene has nothing to do with it. It is a toper’s saying, quite simply, and it is well known that the toper despises milk. All he is asking for here, is not to be condemned to finish with that. It is a glass filled to the brim with red wine that he wants, in order to finish his meal with something pleasant. Not anything else.
     original text:
On s’est fort escrimé sur le vrai sens du dernier précepte. Je crois que l’hygiène n’y est pour rien. C’est un dicton de buveur tout bonnement, et on sait que le buveur méprise le lait. Tout ce qu’il demande ici, c’est de n’être pas condamné à finir par là. C’est un rouge bord qu’il lui faut pour rester sur sa bonne bouche. Pas autre chose.