I am not sure what you are refering to. You absolutely can break Lorentz Invariance in string theory[1]. There is a reason why even some string theory researchers call it the theory of anything.
So A) the paper isn't actually about string theory and B) it's not clear that the claim it makes is actually correct for the field theory it supposedly applies to.
For example you can have string theories that lead to finsler spacetimes, which were used to explain the opera results.