In this paper, we introduce two elicitation approaches for the determination of lex-cel necessary winners (i.e., the elements that are ranked highest according to lex-cel) in a social ranking problem, when the knowledge about preferences over the coalitions is incomplete, and the initially accessible input is a subset of an existing total preorder. The first approach is preorder-driven, and elicitates enough of the underlying total preorder to determine the lex-cel necessary winners. The second approach is element-driven and guides comparisons based on strategically-located coalitions. Finally, we present experimental results and discuss the performance of each approach depending on various parameters and scenarios.