A sequence of positive integers is said to be complete if every positive integer is the sum of a finite number of distinct terms of the sequence. It is well-known that the Lucas sequence \(\{L_j\}\) where \(L_{n+1}=L_n+L_{n-1}\) for \(n>1\) and \(L_0=2\), \(L_1=1\) is complete. In this paper the author proves that if any term \(L_n\), where \(n>1\), is removed from the Lucas sequence the remaining sequence is still complete.