Why is the lower bound for sorting strings Ω(d + nlogn)?
The time complexity you indicated is the lower bound of your specific problem. A lower bound is the worst-case running time of the most optimized TM that recognizes membership in the language.

Lover bound for sorting algorithms is $\Omega(n \log n)$ this means that it is not possible to do better than this and all the sorting cases (instances) may have a temporal complexity $t \geqslant\Omega(n \log n) $. 

For a simple proof of the former lower bound you can take a look at this.