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: 
*The defining quantity for cultural creature lifespan is generation-to-generation data transfer ratio.*

Culture is something to be taught, non-instinct part of a behavior. This means that cultural creature needs to have enough lifetime to:

1. Be taught
2. Apply knowledge to support those who are on stage 1 and 3
3. Teach the next generation

The ratio between these periods varies greatly on the type of civilization. For ancient times (Sparta - Rome) stage 1 was about 10-15 years, stage 2 was about 20 years (since very low productivity) and stage 3 was about 3-5 years (on average - one teacher teaches 3-5 students). For modern time ratio is 20-25 (up to 30-40 for top tech) / 20-30 / 0,001 - 1 (one teacher teaches up to thousand students in their lifetime).

It means that for an ancient civilization minimum average lifespan should be no less than 30-40 years and for modern - no less than 40-55 years.

Lesser lifespans would prevent knowledge from passing through generations and thus culture would simplify and degrade.

But this is true for humans. For, say, cyborg civilization teaching process might be much shorter - about days, and cyborg-years to support cyborg infrastructure be quite small (due to automation) - about, say, 5 years per cyborg. This would give us that 5 years is enough to support and 10 years enough to support and progress this cyborg culture.
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.