Yes, the situation is weird. Yes, it could cause you problems with your paper and also with the other paper. But it is pretty hard to say how it would play out as it depends on who sees the paper (editors, reviewers, ...) and the minute-by-minute timing of things.
But the problem goes deeper than that. Two nearly identical papers out of the same lab at the same time is what is weird here. It should not have happened. There is some mis-communication within the lab that should be fixed. I can't say whether it is a general problem or not, but that should be investigated.
My suggestion isn't very satisfying, however. If you want to maximize your future collaborative opportunities beyond your degree then a way should be found so that this doesn't become a zero-sum game.
One way to do that is to put a hold on publication of both papers and a short period of discussion about going forward. One possibility is to merge the papers (along with the authorship). If your field isn't overly anal about who is "first" author then it should be easy to work out authorship.
I know of one case in CS, and know both parties, where two students at different universities did essentially the same work at the same time and submitted their theses simultaneously, both for graduation and for publication. It was really good work that answered a fundamentally important outstanding question. However, the graduation of both students was held up for a year while people at both universities investigated the situation. It was determined that the work was truly independent and so both graduated and have gone on to great careers. I think that both theses were published though they overlapped considerably. But the determination was not only that the work was independent, but that it was not the case that either should have known about the work of the other. That is to say, it was neither malfeasance nor negligence that caused the issue. But still, it took a year.