Lines can be parallel in a Euclidean system of geometry  But the non-Euclidean system of geometry that has the most empirical verification is regarded by several prominent physicists as correctly describing the universe we inhabit
If these physicists are right, in our universe there are no parallel lines
Only physicists who are not prominent doubt the view that the universe is correctly described by the non-Euclidean system of geometry that has the most empirical verification.