  In [16], we obtained some congruences for Lucas quotients of two infinite
families of Lucas sequences by studying the combinatorial sum $$\sum_{k\equiv
r(\mbox{mod}m)}{n\choose k}a^k.$$ In this paper, we show that the sum can be
expressed in terms of some recurrent sequences with orders not exceeding
$\varphi{(m)}$ and give some new congruences.
