Students requesting to switch partners mid term I'm a TA in a graduate level course. Students in the course have to hand in a weekly assignment which is done in pairs.

A few days ago, one of the students approached the professor and told her that they are not getting along with their partner and requested to join another pair of students, in practice creating a group of three students and leaving their current partner on their own. The professor asked me and the second TA for our opinion in this matter.

When we inquired further, the student stated (roughly) that they think the partner does not take the course seriously, does not put enough effort and expects them to do all the work. They also stated that success in this course is important for them and that they wish to work along with a similarly motivated student. (They named a specific student they would like to work with. That student already has partner so it would make a group of three students.)

While the request itself sounds legitimate, we are reluctant to comply with it, because we are not happy with the idea of students working on assignments in groups of more than two since we think this is unlikely to lead to situations where all students in the group put in a reasonable amount of effort. Also we are concerned of what will happen with the current partner of the student if we comply.
Thirdly, although we have no proof on this matter, both the professor and I independently had the gut feeling that the request might (mind you, I said might, again there's no proof and we may be totally wrong here) also be related to racial tensions.   

A possible solution we were thinking about is to have a conversation with both students and see if we can make them work together in a more productive way.

I will be most grateful for any tips as to how to make this conversation  productive and as pleasant as possible to the students involved.

Also if someone has any other thoughts on this matter such as creative solutions or convincing arguments for/against the obvious solutions such as refusing the request, complying with the request, doing some reshuffling in the pairs in order to be able to comply with the request and still guarantee all students are working in pairs, I will be most grateful.
I would consider asking the student who is not getting along with their partner, whether they would consider leaving their current partner and work on their own from here on out. That way, the student still would have to do all the work on their own, but no longer has someone benefitting from their efforts without contributing.

If the student seriously considers this solution, you can be more confident that the complaint is genuine: if the student would be willing to go it alone, it is quite likely that the contribution of their current partner is near zero. But if the student is not willing to entertain this solution as a serious option, then you can derive the information that their current partner does contribute at least something to the team, and the request looks much less reasonable.

Based on the information you retrieve from this process, you can still decide to allow the student to join a team of three, or reshuffle some other way; asking the question does not commit you to actually make the student work on their own. But it might give you relevant insights.