In this paper, we present a novel perspective towards IR evaluation by proposing a new family of evaluation metrics where the existing popular metrics (e.g., nDCG, MAP) are customized by introducing a query-specific lower-bound (LB) normalization term. While original nDCG, MAP etc. metrics are normalized in terms of their upper bounds based on an ideal ranked list, a corresponding LB normalization for them has not yet been studied. Specifically, we introduce two different variants of the proposed LB normalization, where the lower bound is estimated from a randomized ranking of the corresponding documents present in the evaluation set. We next conducted two case-studies by instantiating the new framework for two popular IR evaluation metric (with two variants, e.g., DCG_UL_V1,2 and MSP_UL_V1,2 ) and then comparing against the traditional metric without the proposed LB normalization. Experiments on two different data-sets with eight Learning-to-Rank (LETOR) methods demonstrate the following properties of the new LB normalized metric: 1) Statistically significant differences (between two methods) in terms of original metric no longer remain statistically significant in terms of Upper Lower (UL) Bound normalized version and vice-versa, especially for uninformative query-sets. 2) When compared against the original metric, our proposed UL normalized metrics demonstrate higher Discriminatory Power and better Consistency across different data-sets. These findings suggest that the IR community should consider UL normalization seriously when computing nDCG and MAP and more in-depth study of UL normalization for general IR evaluation is warranted.