Without further context and using only the fact that the author was not particularly fond of the tool, it could mean one of the following.
(1) He liked it very much in the past but dislikes it now.
(2) He found it difficult to use but has mastered it now.
(3) He had a bad time using it but is not troubled by it now.
Edit: found the citation from 1672, from Andrew Marvell’s The Rehearsal Transpros'd:
Two or three brawny Fellows in a
Corner, with meer Ink and
Elbow-grease, do more Harm than an
Hundred systematical Divines with
their sweaty Preaching.
It's also defined in B.E.'s A New Dictionary of the Terms Ancient and Modern of the Canting Crew, in its several tribes, of gypsies, beggers, thieves, cheats, &c. with an addition of some proverbs, phrases, figurative speeches, &c., c.1698:
Elbow-greaſe, a deriſory term for
Sweat. It will coſt nothing but a
little Elbow-grease ; in a jeer to one
that is lazy, and thinks much of his
Labour.
I found no earlier mentions than senderle, but here are some useful references. These are the earliest references I could find, and helpfully, they are also dictionary definitions.
The Online Etymology Dictionary says
Phrase elbow grease "hard rubbing" is
attested from 1670s, from jocular
sense of "the best substance for
polishing furniture."
There's a similarly colourful definition in Francis Grose's 1785 A Classical Dictionary of the Vulgar Tongue:
ELBOW GREASE, labour, elbow grease
will make an oak table shine.
(The rest of this dictionary is interesting too!)
Also, very pertinent to the question, here's The Royal Dictionary, French and English, and English and French by Abel Boyer in 1729:
Elbow-grease, (or Pains) Rude travail.
Rude travail is French for rough work. There's no entry for "l'huile de coude" in the French side.
And in John S. Farmer and W.E. Henley's 1905 A Dictionary of Slang and Colloquial English:
Elbow-grease. Energetic and continuous
manual labour : e.g. Elbow-grease is
the best furniture oil : Fr., huile de
bras or de poignet ; du foulage
(1779).
French huile de bras or de poignet is oil of the arm, wrist which is quite close. I think du foulage is fulling, the manual scouring and milling of cloth.
The earliest French reference I could "l'huile de coude" helpfully explains the term. In Jean Humbert's 1852 Nouveau Glossaire Genevois: Volume 1 (New Geneva Glossary):
Dans le langage badin des domestiques
et des maîtresses, l'huile de coude,
c'est le frottage, c'est-à-dire : Le
travail de la servante qui frotte.
Ces meubles, Madame, ne veulent pas
devenir brillants. — C'est que, ma
mie, tu y as sans doute économisé
l'huile de coude; c'est-à-dire : Tu as
trop ménagé ton bras et tes forces.
A rough translation:
In the playful language of servants
and masters, elbow grease is rubbing,
i.e. the work of the maid
who scrubs. This furniture, Madam,
does not want to shine. - My dear,
that is because you have undoubtedly
skimped on the elbow grease. In other
words, you have conserved both your arm and
your strength.
These references also suggest that "l'huile de coude" is an anglicisme.
Best Answer
It's normally heard as Shall I be mother? meaning 'Shall I pour the tea?' It's used because pouring the tea has traditionally been seen as a mother's role. I suspect it's now heard less than it once was for various social rather than linguistic reasons. It's not slang and it's not facetious, but because of the nature of tea-drinking it's likely to be heard in informal situations.