A complete certainty.
The 'cinch' that this expression derives from is the Spanish/Mexican word for a horse's saddle-girth - cincha. These were typically made from twisted strands of horsehair and provided a secure fixing for the saddle. The word is recorded in English, as 'synch' and later 'cinch' in various US sources from the 1860s onward. From the 1880s the use was extended into a verb form and things which were tightly secured were said to be 'cinched'; for example, this piece from The Manitoba Daily Free Press, December 1882:
"The next movement was to throw the bull, and then cinch a lasso and rope tightly around his body."
The figurative use of cinch, meaning to tie-up or make certain, in non-animal contexts began around the same time. The usage was often in contexts where the rich and powerful used their status to form monopolies or indulge in insider trading in order to cheat the general public. An example of this comes from the Illinois newspaper The Morning Review, December 1889, which is the earliest citation of 'lead-pipe cinch' that I've found:
"The briber and bribed would sit down to a game of poker and a "lead-pipe cinch" was nothing to the sure thing the legislators had."
The common usage of 'cinch' now, that is, to mean 'easy' rather than 'secure', comes from this 'easy money' association.
The 'cinch' part of the phrase is fairly straightforward, but what about 'lead-pipe'. On the face of it there doesn't seem to be anything especially secure or easy about lead pipes. Some have suggested that lead pipes were used to twist and tighten cinch straps. That seems difficult to understand, as virtually any nearby piece of wood could have been used just as well. Another explanation is that a cinch was a form of joint used in plumbing and that a lead-pipe cinch was a secure joint. I can find no record of that name for a plumbing joint, either recent or from the late 19th century and, lacking evidence, that has to be classed as speculative. Others have suggested the derivation lied with some property of lead pipe, for example, it is easy to bend, or it constituted an effective weapon with the certainty of knocking someone out. Again, there's no evidence for these suggestions.
It seems more likely that there's no particular reason that 'lead-pipe' was chosen as an intensifier for cinch, other than it trips nicely off the tongue. In support of that view there are examples of other intensifiers for cinch, which would hardly be likely if 'lead-pipe' had a special meaning. In 1891, Maitland's Slang Dictionary refers to 'leadpipe' and 'grapevine' as superlatives for cinch. In October the same year The Daily Morning Republican, listed a number of 'cinch' superlatives to describe a punter's certainty that his horse Firenzo would win the next day:
"The track will be heavy tomorrow, and I've got a copper riveted, lead pipe, copyrighted, air tight cinch. Firenzo in the mud - she swims in it."