We carry out Faddeev calculations of three-alpha (3 alpha) and two-alpha plus Lambda (alpha alpha Lambda) systems, using two-cluster resonating-group method kernels. The input includes an effective two-nucleon force for the alpha alpha resonating-group method and a new effective Lambda N force for the Lambda alpha interaction. The latter force is a simple two-range Gaussian potential for each spin-singlet and triplet state, generated from the phase-shift behavior of the quark-model hyperon-nucleon interaction, fss2, by using an inversion method based on supersymmetric quantum mechanics. Owing to the exact treatment of the Pauli-forbidden states between the clusters, the present three-cluster Faddeev formalism can describe the mutually related, alpha alpha, 3 alpha and alpha alpha Lambda systems, in terms of a unique set of the baryon-baryon interactions. For the three-range Minnesota force which describes the alpha alpha phase shifts quite accurately, the ground-state and excitation energies of 9Be Lambda are reproduced within 100 - 200 keV accuracy.
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