For a graph ( ) total edge Lucas irregular labeling f :V(G) ?E (G) ? {1,2,…,K} is defined as a labeling on V(G) and E (G) in such a way that for any two different edges and , their weights ( ) ( ) ( ) and ( ) ( ) ( ) are distinct Lucas numbers.The total edge Lucas irregularity strength, tels(G), is defined as the minimum K for which G has total edge Lucas irregular labeling. In this paper we prove the graphs , Cn ,K1,n and Book (with 3 sides and 4 sides) admits total edge Lucas irregular labeling and we determine the total edge Lucas irregularity strength for those graphs.