This paper studies some sums of products of the Lucas numbers. They are a generalization of the sums of the Lucas numbers, which were studied another authors. These sums are related to the denominator of the generating function of the kth powers of the Fibonacci numbers. We considered a special case for an even positive integer k in the previous paper and now we generalize this result to an arbitrary positive integer k. These sums are expressed as the sum of the binomial and Fibonomial coefficients. The proofs of the main theorems are based on special inverse formulas.