All the livelong day: the expression is actually generally used with a negative connotation, to refer to a period of time that is too long, too tiring:
- all day long. Well, of course you get to feeling stiff, sitting in front of a computer all the livelong day. I'd go crazy if I had to stay at home all the livelong day.
(McGraw-Hill Dictionary of American Idioms and Phrasal Verbs)
According to the Phrase Finder the folksong "I've Been Working on the Railroad"(1936) you cite may be responsible for its origin, but the expression was actually used well before that date and the term 'livelong' has a complex and ancient origin.
The following source says that the origin of the adjective"lifelong" is quite old and it originally meant, "dear, beloved". Only in the late 18th century its meaning changes to "lifetime, lifelong" probably as a result of a misanalysys of the word's origin:
Livelong is not a common adjective. Its use, for the most part, is restricted to one expression, all the livelong day, although as late as the nineteenth century the livelong night was also common. In these expressions the word is simply an intensified version of the adjective long. But why live-? We don’t use that word to intensify anything else.
- Well, the word goes back to the first half of the fifteenth century. Livelong is first recorded in Henry Lovelich’s poem The History of the Holy Grail, found in the manuscript Cambridge, Corpus Christi College 80:
And thus vppon the yl stood Nasciens there Al the live long day In this Manere.
(And thus upon the hill stood the nations there all the livelong day in this manere.
- Al that leve longe Nyht Into the Se he loked forth Ryht
(All that livelong night he looked directly into the sea.)
Lovelich probably penned the poem around 1410. The manuscript dates from before 1450. And the date provides us with a clue for why live- is used in the word.
The live- in livelong does not refer to living. Instead, it’s from the Old English leof, meaning dear, beloved. It shares a common Germanic root with the Old English lufu, or love.
There is a less common use of livelong to mean for a lifetime or lifelong. This sense appears in the late eighteenth century and would appear to be the result of a misanalysis of the word’s origin.
Ngram, all the livelong day can be found from the late 18th century.
1786 Burns Twa Dogs 295 Or lee-lang nights, wi crabbit leuks, Pore owre the devil's pictur'd beuks.
1787 F. Burney Diary June, This was the last day of freedom for the whole livelong summer.
1806 J. Grahame Birds Scot. 77 The live long summer day She at the house end sits.
- 1829 Hogg Sheph. Cal. I. 25 He watched there the lee-lang night.
- 1847 Emerson Poems, Good-bye Wks. (Bohn) I. 416 Where arches green, the livelong day, Echo the blackbird's roundelay.
- 1870 Bryant Iliad I. ii. 35 It ill becomes a chief To sleep the livelong night