The running time of counting sort is Θ (n+k). If k=O(n), the algorithm is O(n). The k represents the range of the input elements. 
Can I say that the Counting sort has a lower bound of O(n) because the algorithm takes O(n) time to compute a problem and that the lower bound of O(n) shows that there is no hope of solving a specific computation problem in time better than Ω(n)??