We are concerned with the ideas of pairwise Lindelöf, generalizations of pairwise Lindelöf and pairwise regular-Lindelöf in bitopological space. There are four kinds of pairwise Lindelöf, i.e., Lindelöf, B-Lindelöf, s-Lindelöf and p-Lindelöf and three kinds of generalized pairwise Lindelöf, i.e., pairwise nearly Lindelöf, pairwise almost Lindelöf and pairwise weakly Lindelöf. Another idea is leads to the pairwise nearly regular-Lindelöf, pairwise almost regular-Lindelöf and pairwise weakly regular-Lindelöf. Some characterizations of these new spaces are given. The relations among them are studied. Subspaces are also studied and some of their characterizations investigated. We show that some subsets inherit these generalized pairwise covering properties. Mappings and generalized pairwise continuities are also studied. The effect of mappings on these generalized properties is investigated. We show that some mappings preserve these pairwise covering properties. It is shown that some of the generalized properties are pairwise semiregular properties. The productivity of these generalized properties are studied. We show that the pairwise Lindelöf are not preserved under finite products.