In this article we show that a contra second countable bitopological space is a p1-Lindelöf space, but the converse part is not necessarily true in general. We provide suitable example with the help of concepts of nest and interlocking from other areas related to bitopology. The relation between pairwise regular spaces and p 1 -normal spaces has been investigated. Finally, we propose some open problems which may enrich various concepts related to Lindelöfness in a bitopological space and other areas of mathematical ideas.