Question: I was brainstorming with a bunch of friends about a story with more than one sapient species on a planet. The idea was to have different lifespans for each species as part of their differences.

I thought about having the usual humans with a standard 70 years lifespan and other species with ten (10) or a hundred (100) times longer lifespans but then the idea of a species with a shorter lifespan came up.

These species are supposed to be able to create a fully functional civilization with culture and some technology and given that most cultural and intellectual endeavors and most skills, blacksmithing, for example, take a lot of time to developed I worried that if we made their average lifespan too short they would not be able to form any sort of civilization.

My question is: what do you think is the minimal lifespan that would allow a species to develop a functional human-like civilization? By this I mean they have some sort of culture like music and religion and technology, like metalworking or masonry, academic pursuits like mathematics and science, and functioning governments and economies et cetera.

Also these species are also as smart as humans, if they are super geniuses then the question is pointless. And lack magic or superpowers that could let them transplant knowledge from other individuals into themselves. Basically they cannot cheat to learn stuff

Answer: 
I think the lifespan should be such that 3 generations can coexist at any time, allowing the grandparents to help the parents in raising the children.

This would allow for a more efficient transmission of knowledge through the generations and resource collection, since the parents can dedicate more time to it instead of chasing the babies.

Thus, if sexual maturity is reached at X years of age, the lifespan should be at least 3X.
Firstly, lifespan doesn't matter in isolation, as pointed out by other answers. What matters is lifespan should be long enough for learning to take place from parent to child.

How quickly this learning takes place could be anything. There could be an option to acquire the entire brain of the parent. Alternatively the species as a whole might share a brain (like if corals or banyan trees had brains). Or maybe children share their brain with just their parents, and branch off (like plant offshoots). If learning must take place via outside media, how about it being chemical? We use oral and non-verbal communication which is relatively slow, direct chemical communication could be much faster.

The parent need not be alive for the children to learn. Mammals have a take-care-of-young-for-long principle, most species don't. Parents could leave non-living remnants for children to study in their own time. (For instance if your parent taught you basic reading skills then died - leaving you the knowledge of the internet; not a perfect example cause we have emotional needs but what if we didn't). Survival skills can be genetically coded instead of having to be learnt from parents (like with most species except mammals), everything else can be learnt via a non-living medium such as written text.