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You can unroll the construction for L to an early break:

def l_kcycles(G,l,k):
    H = graphs.CycleGraph(k)
    L = set()
    for g in G.subgraph_search_iterator(H, induced=False):
        L.add( tuple(g.edges(labels=False,sort_vertices=True,sort=True)) )
        if len(L)>l:
            return False
    return len(L)==l