Should I ask a reference letter from someone working where I am applying to use it for another application? I am applying to a PhD program. I worked in the past with researcher A from research team T who was my bachelor thesis supervisor. Now, I am applying to a PhD progam within the research team T and also to another universities. 

Researcher A would be a perfect candidate to ask for a reference letter, since my internship under his supervision went really well. However, I am wondering whether or not it would be appropriate to ask him, since I would use it to apply to other universities (he would know that of course).

Details: 


I already applied at team T and am waiting for news. 
A is not the team director but the team is quite small and A knows I applied there. 
A is not the one who would supervise the PhD I applied to.


I am afraid that asking him for a reference letter could make him think that I am not that much interested in that lab L and that this could have a negative impact on my application at this lab.
I understand your hesitation and there may be situations in which your concerns are spot on. That said, people in the position of researcher A exist to support and further the successful outcomes of their students. Outside specific research contributions, this is their legacy. One of the most rewarding aspects of leadership is helping people succeed. 

Based on your question, I recommend immediately asking researcher A for a recommendation letter. Discuss any concerns with them directly and save yourself the worrying. You can always draft the letter for them and let them make revisions as they see fit. 

Good luck!