Lynkaeus is the son of Herakles and Tiphyse who was one of King Thespius. During his stay in the court of King Thespius Herakles impregnated 49 of 50 Thespius' daughters including Aeskhreis who he lay with one night. The result of that particular encounter was Lynkaeus.
"by Tiphyse he [Herakles] had Lynkaeus"
- Apollod. Biblioteca 2.7.8