If space is circular then time must, as well, be circular, and relativity won’t work any more.
We have said that from our perspectives, clocks that are forward in the direction of motion are lagging behind clocks that are backward. When space is circular, there won’t be “forward” and “backward” anymore, and so we will need to modify relativity and Lorentz Transformation to account for that.
For a mathematical example, assume Lambda=13/5, then if Gracie travels 5 years to get back to George, she will find his clock to be t’ = lambda(t – xv/c^2) = lambda(t – 0) = 13, but George will find the same result, and will say that Gracie has passed 13 years. Leading to an actual paradox this time