Diophantine equations with products of consecutive terms in Lucas sequences

In this paper, we show that if (un)n⩾1 is a Lucas sequence, then the Diophantine equation un·un+1⋯··un+k=ym in integers n⩾1, k⩾1, m⩾2 and y with |y|>1 has only finitely many solutions. We also determine all such solutions when (un)n⩾1 is the sequence of Fibonacci numbers and when un=(xn-1)/(x-1) for all n⩾1 with some integer x>1.