In which situations can I claim that additional data is needed for an existing research paper? I wanted to write about a certain computer science topic, and after a while I figured out that the same research question was taken already. Still, I think that not all problems where addressed in this paper so I believe there's still room for me to conduct my research, and additional data would do be needed. Also, looking at the current research paper, I think it lacks enough motivation.

I'm finding it tricky to justify that. Any help or similar experiences are appreciated.
A paper rarely addresses all problems and it is normal for other papers to follow. 

However, a paper that lacks motivation needn't demand a subsequent paper. That said, you might be able to identify new applications for the paper, which could merit a new paper.

If you're finding it tricky to justify [a new paper], then perhaps no new paper is needed.