Translation:Grandfather died in the middle of the last decade.
Even "the last decade" would work, but it definitely needs the article.
Does it? I mean "in the middle of last year" works. Can we say for sure "last decade" can't work as well?
I have never heard it or seen it written. English has no language authority like the Academie Francaise, so if some native English-speaker says this somewhere, then it can work, in a sense. I would at least point out that this is not standard in the larger English-speaking populations.
We say yesterday morning, yesterday afternoon, and yesterday evening, but last night, last week, last month, and last year, and the last decade, the last century, and the last millennium.