Implement a min heap using a list of lists

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C++11

I'm trying to implement a min heap using a list of lists of integers. I have working code to do as such but My code is not efficient enough. I was wondering I someone could help me optimize my code as I have no idea what to do at this point.

Note: Every list is already ordered in ascending order.

What I have tried:

void organizeLists(std::vector<std::list<int>>& lists, std::vector<int>& output) {
    Comp comp;
    for (std::vector<std::list<int>>::iterator listMember=lists.begin(); listMember!=lists.end();) {
        if(listMember->empty()) {
            listMember = lists.erase(listMember);
        } else {
            ++listMember;
        }
    }
    if(!lists.empty()) {
        std::make_heap(lists.begin(), lists.end(), comp);
        while (!lists.empty()) {
            std::list<int> &temp = lists.front();
            output.push_back(temp.front());
            temp.pop_front();
            if (temp.empty()) {
                lists.erase(lists.begin());
            }
            std::make_heap(lists.begin(), lists.end(), comp);
        }
    }
}