What's the origin of the phrase - "For the life of me"?

The ODO definition is:

(informal) However hard I try; even if my life depended on it

I have come across this phrase quite a lot of times in EL&U:

• For the life of me, I can't remember that word...

• I can't, for the life of me, find an idiom...

and so on.

I tried to visualize it via Ngram plots and it indicates that the usage started somewhere around early 1760s but can't pin-point an exact source or timeline.

Is there any interesting etymology behind this expression?

Solution 1:

OED has an entry for:

for (one's) life (also for dear life, etc.): as if, or in order to, save one's life.

and adds that:

Also hyperbolically in trivial use: (I cannot) for my life, (I cannot) for the life of me.

The early forms for (one's) life and for dear life were used literally and OED's earliest example is from c1275:

Þat he ne miȝte for his liue Iso þat man wiþ hire speke.

_{John Henry Grafton Grattan · The Owl and the Nightingale.}

OED's citation from 1632 might be the first idiomatic usage:

For my life I could neuer attaine to any perfect knowledge thereof.

_{William Lithgow · The totall discourse..of..trauayles, from Scotland, to..Europe, Asia, and Affrica}