Final answer:
In Euripides' Herakles, the illegitimate tyrant is Lycus, the usurper king of Thebes.
Step-by-step explanation:
In Euripides' play Herakles, the character presented as an illegitimate tyrant is Lycus. Lycus is the usurper king of Thebes who seizes power after the death of Herakles' father, Amphitryon. He rules with cruelty and violence, oppressing the people of Thebes.