According to the formal statement of the lemma here:
https://en.wikipedia.org/wiki/Pumping_lemma_for_regular_languages
It is written at (3) that for all $i≥0, xy^iz∈L$.
Until this moment, I was certain that $i$ must be a natural number.
But what if, for example, $|y|=4$ and I want to pick $i=2.5$. Is that possible to pick an $i$ which is not an integer?
I will get a valid length, and it looks ok by definition, however that seems strange to me that I can perform $y^i$ with an i that isn't an integer.
You are right; $i$ must be a natural number.
It is quite often the case in mathematical writing that there are implicit assumptions. The reader is then supposed to know them or infer them from the context. In this case, you - the OP - in fact did know that $i$ was supposed to be a natural number :-).