If there are two I(1) series that are not cointegrated, why could it be that if I create a VECM and impose restrictions implying that they are cointegrated, that I cannot reject this restriction according to the LR test? Could this be a spurious result, or generally how could I explain this theoretically?
You are testing whether restrictions within a VECM hold, which is not directly related to testing for cointegration. These are two different things. If the series are not cointegrated, you are comparing one inappropriate model to another inappropriate model, and the test result tells you that there is little difference between these two models. But it does not tell you that there is cointegration.