I haven't been able to find any clear guidance on this. To me, life span looks wrong, but I have no evidence to support my intuition.
A tentative look (webster vs oxford) suggests that perhaps BrE vs AmE may play a role in this, but it's not particularly clear.
Might there also perhaps be a small semantic difference between them meaning the usage depends on context? I haven't managed to find anything which indicates this is the case.
It is mainly a matter of style not definition.
Per Merriam-Webster (US):
life span
1 : the average length of life of a kind of organism or of a material object especially in a particular environment or under specified circumstances
2 : the duration of existence of an individual
Per Oxford (UK):
lifespan
The length of time for which a person or animal lives or a thing functions. ‘the human lifespan’
Although Merriam-Webster gives two senses, the essential meaning seems to be the same.
If I had to say what's different about M-W's first sense, I'd say that it's—for some reason—making a distinction between contextual and "normal" lifespans.
To contrast this slightly, the Canadian Oxford Dictionary also lists a single sense [I am transcribing this from my physical copy]:
lifespan
the length of time for which a person or creature lives, or for which a thing exists or is functional
The only essential difference is the regional style in which it's presented—either in an open form or a closed form.
For all intents and purposes, the langauge is the same. It's just that you will spell (or punctuate) it differently depending on which part of the world your audience is located in. (If you are in the US, it is spelled in an open form; if you're in the UK, it uses a closed form.)
Let's have a look at Google Ngrams:
Here we see that "life span" does seem to be the more popular choice, but "lifespan" is growing in usage.
