The entry in _Der Kleine Pauly_ seem to indicate that there are only three surviving places where he is mentioned. Here they are:
Proclus, Commentary on the First Book of Euclid's Elements, 66: "At this time [Plato's time] also lived Leodamas of Thasos, Archytas of Tarentum, and Theaetetus of Athens, by whom the theorems [of geometry] were increased in number and brought into a more scientific arrangement. Younger than Leodamas was Neoclides and his pupil Leon, who added many discoveries. .... (67) Eudoxus of Cnidus, a little later than Leon, ..." (transl. G. R. Morrow)
Proclus, op. cit., 211: "Plato, it is said, taught this method [analysis] to Leodamas, who is also reported to have made many discoveries in geometry by means of it."
Diogenes Laertius 3, 24: "He [Plato] was the first to explain to Leodamas of Thasos the method of solving problems by analysis."